[{"ddc":["510"],"related_material":{"record":[{"relation":"earlier_version","id":"10013","status":"public"}]},"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"external_id":{"isi":["000975817300002"],"arxiv":["2108.01733"]},"title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","ec_funded":1,"doi":"10.4171/IFB/484","year":"2023","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","publication_identifier":{"eissn":["1463-9971"],"issn":["1463-9963"]},"_id":"13043","article_processing_charge":"No","date_updated":"2023-08-01T14:43:29Z","oa":1,"volume":25,"arxiv":1,"author":[{"orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","last_name":"Hensel","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Laux, Tim","last_name":"Laux","first_name":"Tim"}],"abstract":[{"lang":"eng","text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction\r\nof a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting along triple junctions."}],"citation":{"mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>Interfaces and Free Boundaries</i>, vol. 25, no. 1, EMS Press, 2023, pp. 37–107, doi:<a href=\"https://doi.org/10.4171/IFB/484\">10.4171/IFB/484</a>.","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>Interfaces and Free Boundaries</i>. 2023;25(1):37-107. doi:<a href=\"https://doi.org/10.4171/IFB/484\">10.4171/IFB/484</a>","ista":"Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.","short":"S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” <i>Interfaces and Free Boundaries</i>, vol. 25, no. 1. EMS Press, pp. 37–107, 2023.","apa":"Hensel, S., &#38; Laux, T. (2023). Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>Interfaces and Free Boundaries</i>. EMS Press. <a href=\"https://doi.org/10.4171/IFB/484\">https://doi.org/10.4171/IFB/484</a>","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>Interfaces and Free Boundaries</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/IFB/484\">https://doi.org/10.4171/IFB/484</a>."},"publication_status":"published","file":[{"date_updated":"2023-05-22T07:24:13Z","access_level":"open_access","date_created":"2023-05-22T07:24:13Z","checksum":"622422484810441e48f613e968c7e7a4","file_name":"2023_Interfaces_Hensel.pdf","file_size":867876,"creator":"dernst","file_id":"13045","content_type":"application/pdf","relation":"main_file","success":1}],"date_created":"2023-05-21T22:01:06Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"EMS Press","date_published":"2023-04-20T00:00:00Z","article_type":"original","month":"04","file_date_updated":"2023-05-22T07:24:13Z","page":"37-107","publication":"Interfaces and Free Boundaries","issue":"1","status":"public","intvolume":"        25","type":"journal_article","day":"20"},{"type":"journal_article","day":"01","status":"public","intvolume":"        24","file_date_updated":"2022-08-16T06:55:22Z","issue":"3","publication":"Journal of Mathematical Fluid Mechanics","date_published":"2022-08-01T00:00:00Z","article_type":"original","month":"08","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","department":[{"_id":"JuFi"}],"has_accepted_license":"1","date_created":"2022-08-14T22:01:45Z","file":[{"file_size":2045570,"file_name":"2022_JMathFluidMech_Hensel.pdf","checksum":"75c5f286300e6f0539cf57b4dba108d5","date_created":"2022-08-16T06:55:22Z","access_level":"open_access","date_updated":"2022-08-16T06:55:22Z","success":1,"relation":"main_file","content_type":"application/pdf","file_id":"11848","creator":"cchlebak"}],"publication_status":"published","citation":{"chicago":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00021-022-00722-2\">https://doi.org/10.1007/s00021-022-00722-2</a>.","apa":"Hensel, S., &#38; Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00021-022-00722-2\">https://doi.org/10.1007/s00021-022-00722-2</a>","ieee":"S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 24, no. 3. Springer Nature, 2022.","ista":"Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 24(3), 93.","short":"S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).","ama":"Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. <i>Journal of Mathematical Fluid Mechanics</i>. 2022;24(3). doi:<a href=\"https://doi.org/10.1007/s00021-022-00722-2\">10.1007/s00021-022-00722-2</a>","mla":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 24, no. 3, 93, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s00021-022-00722-2\">10.1007/s00021-022-00722-2</a>."},"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","last_name":"Hensel","full_name":"Hensel, Sebastian","first_name":"Sebastian"},{"id":"25647992-AA84-11E9-9D75-8427E6697425","first_name":"Alice","full_name":"Marveggio, Alice","last_name":"Marveggio"}],"abstract":[{"lang":"eng","text":"We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids."}],"oa":1,"volume":24,"date_updated":"2023-11-30T13:25:02Z","article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors warmly thank their former resp. current PhD advisor Julian Fischer for the suggestion of this problem and for valuable initial discussions on the subjects of this paper. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"quality_controlled":"1","_id":"11842","publication_identifier":{"issn":["1422-6928"],"eissn":["1422-6952"]},"ec_funded":1,"doi":"10.1007/s00021-022-00722-2","year":"2022","title":"Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities","external_id":{"isi":["000834834300001"],"arxiv":["2112.11154"]},"article_number":"93","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"related_material":{"record":[{"status":"public","id":"14587","relation":"dissertation_contains"}]}},{"day":"24","type":"journal_article","intvolume":"        61","status":"public","issue":"6","publication":"Calculus of Variations and Partial Differential Equations","file_date_updated":"2023-01-20T08:56:01Z","month":"08","article_type":"original","date_published":"2022-08-24T00:00:00Z","publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"JuFi"}],"file":[{"success":1,"file_id":"12320","creator":"dernst","relation":"main_file","content_type":"application/pdf","checksum":"b2da020ce50440080feedabeab5b09c4","date_created":"2023-01-20T08:56:01Z","file_size":1278493,"file_name":"2022_Calculus_Hensel.pdf","access_level":"open_access","date_updated":"2023-01-20T08:56:01Z"}],"date_created":"2022-09-11T22:01:54Z","publication_status":"published","citation":{"short":"S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations 61 (2022).","ista":"Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. 61(6), 201.","mla":"Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 6, 201, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s00526-022-02307-3\">10.1007/s00526-022-02307-3</a>.","ama":"Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. <i>Calculus of Variations and Partial Differential Equations</i>. 2022;61(6). doi:<a href=\"https://doi.org/10.1007/s00526-022-02307-3\">10.1007/s00526-022-02307-3</a>","chicago":"Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00526-022-02307-3\">https://doi.org/10.1007/s00526-022-02307-3</a>.","apa":"Hensel, S., &#38; Moser, M. (2022). Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-022-02307-3\">https://doi.org/10.1007/s00526-022-02307-3</a>","ieee":"S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 6. Springer Nature, 2022."},"abstract":[{"text":"We extend the recent rigorous convergence result of Abels and Moser (SIAM J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to 90∘. We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π). For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order ε; again for general contact angles α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen–Cahn operator. Instead, we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233, 2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer et al. (arXiv:2003.05478v2).","lang":"eng"}],"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","full_name":"Hensel, Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072"},{"last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c"}],"oa":1,"volume":61,"date_updated":"2023-08-03T13:48:30Z","article_processing_charge":"No","_id":"12079","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"This Project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 948819)  , and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1 - 390685813.\r\nOpen Access funding enabled and organized by Projekt DEAL.","oa_version":"Published Version","quality_controlled":"1","project":[{"grant_number":"948819","call_identifier":"H2020","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"year":"2022","doi":"10.1007/s00526-022-02307-3","ec_funded":1,"external_id":{"isi":["000844247300008"]},"title":"Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"article_number":"201","ddc":["510"]},{"ddc":["510"],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"title":"Finite time extinction for the 1D stochastic porous medium equation with transport noise","external_id":{"isi":["000631001700001"]},"ec_funded":1,"year":"2021","doi":"10.1007/s40072-021-00188-9","acknowledgement":"This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem as well as helpful discussions. Special thanks go to F. Cornalba for suggesting the additional κ-truncation in Proposition 5. I am also indebted to an anonymous referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning the treatment of the noise term). The issue is resolved in this version.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","oa_version":"Published Version","_id":"9307","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"volume":9,"date_updated":"2023-08-07T14:31:59Z","oa":1,"article_processing_charge":"Yes (via OA deal)","author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","last_name":"Hensel","first_name":"Sebastian"}],"abstract":[{"text":"We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.","lang":"eng"}],"publication_status":"published","citation":{"short":"S. Hensel, Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021) 892–939.","ista":"Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 9, 892–939.","ama":"Hensel S. Finite time extinction for the 1D stochastic porous medium equation with transport noise. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2021;9:892–939. doi:<a href=\"https://doi.org/10.1007/s40072-021-00188-9\">10.1007/s40072-021-00188-9</a>","mla":"Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 9, Springer Nature, 2021, pp. 892–939, doi:<a href=\"https://doi.org/10.1007/s40072-021-00188-9\">10.1007/s40072-021-00188-9</a>.","chicago":"Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s40072-021-00188-9\">https://doi.org/10.1007/s40072-021-00188-9</a>.","ieee":"S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation with transport noise,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 9. Springer Nature, pp. 892–939, 2021.","apa":"Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium equation with transport noise. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-021-00188-9\">https://doi.org/10.1007/s40072-021-00188-9</a>"},"date_created":"2021-04-04T22:01:21Z","file":[{"date_updated":"2021-04-06T09:31:28Z","access_level":"open_access","file_name":"2021_StochPartDiffEquation_Hensel.pdf","file_size":727005,"date_created":"2021-04-06T09:31:28Z","checksum":"6529b609c9209861720ffa4685111bc6","content_type":"application/pdf","relation":"main_file","file_id":"9309","creator":"dernst","success":1}],"department":[{"_id":"JuFi"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","date_published":"2021-03-21T00:00:00Z","article_type":"original","month":"03","file_date_updated":"2021-04-06T09:31:28Z","page":"892–939","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","status":"public","intvolume":"         9","type":"journal_article","day":"21"},{"file_date_updated":"2021-09-15T14:37:30Z","page":"300","type":"dissertation","day":"14","supervisor":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"}],"status":"public","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"degree_awarded":"PhD","has_accepted_license":"1","file":[{"content_type":"application/x-zip-compressed","relation":"source_file","file_id":"10008","creator":"shensel","date_updated":"2021-09-15T14:37:30Z","access_level":"closed","file_name":"thesis_final_Hensel.zip","file_size":15022154,"date_created":"2021-09-13T11:03:24Z","checksum":"c8475faaf0b680b4971f638f1db16347"},{"access_level":"open_access","date_updated":"2021-09-14T09:52:47Z","checksum":"1a609937aa5275452822f45f2da17f07","date_created":"2021-09-13T14:18:56Z","file_size":6583638,"file_name":"thesis_final_Hensel.pdf","file_id":"10014","creator":"shensel","relation":"main_file","content_type":"application/pdf"}],"date_created":"2021-09-13T11:12:34Z","date_published":"2021-09-14T00:00:00Z","month":"09","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","oa":1,"date_updated":"2023-09-07T13:30:45Z","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"issn":["2663-337X"]},"_id":"10007","citation":{"chicago":"Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10007\">https://doi.org/10.15479/at:ista:10007</a>.","apa":"Hensel, S. (2021). <i>Curvature driven interface evolution: Uniqueness properties of weak solution concepts</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10007\">https://doi.org/10.15479/at:ista:10007</a>","ieee":"S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021.","ista":"Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.","short":"S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.","ama":"Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10007\">10.15479/at:ista:10007</a>","mla":"Hensel, Sebastian. <i>Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10007\">10.15479/at:ista:10007</a>."},"publication_status":"published","author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","last_name":"Hensel","full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072"}],"abstract":[{"lang":"eng","text":"The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis."}],"alternative_title":["ISTA Thesis"],"ddc":["515"],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10012"},{"status":"public","id":"10013","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"7489"}]},"ec_funded":1,"doi":"10.15479/at:ista:10007","year":"2021","title":"Curvature driven interface evolution: Uniqueness properties of weak solution concepts"},{"article_processing_charge":"No","date_updated":"2023-05-03T10:34:38Z","oa":1,"publication":"arXiv","arxiv":1,"oa_version":"Preprint","project":[{"grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. The content of this paper was developed and parts of it were written during a visit of the first author to the Hausdorff Center of Mathematics (HCM), University of Bonn. The hospitality and the support of HCM are gratefully acknowledged.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10011","type":"preprint","day":"09","citation":{"ista":"Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. arXiv, 2109.04233.","short":"S. Hensel, T. Laux, ArXiv (n.d.).","ama":"Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2109.04233\">10.48550/arXiv.2109.04233</a>","mla":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of  the Allen-Cahn Equation and Weak-Strong Uniqueness.” <i>ArXiv</i>, 2109.04233, doi:<a href=\"https://doi.org/10.48550/arXiv.2109.04233\">10.48550/arXiv.2109.04233</a>.","chicago":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of  the Allen-Cahn Equation and Weak-Strong Uniqueness.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2109.04233\">https://doi.org/10.48550/arXiv.2109.04233</a>.","apa":"Hensel, S., &#38; Laux, T. (n.d.). A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2109.04233\">https://doi.org/10.48550/arXiv.2109.04233</a>","ieee":"S. Hensel and T. Laux, “A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness,” <i>arXiv</i>. ."},"publication_status":"submitted","keyword":["Mean curvature flow","gradient flows","varifolds","weak solutions","weak-strong uniqueness","calibrated geometry","gradient-flow calibrations"],"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian"},{"first_name":"Tim","full_name":"Laux, Tim","last_name":"Laux"}],"status":"public","abstract":[{"text":"We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow - is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2109.04233"}],"article_number":"2109.04233","department":[{"_id":"JuFi"}],"date_created":"2021-09-13T12:17:10Z","ec_funded":1,"date_published":"2021-09-09T00:00:00Z","doi":"10.48550/arXiv.2109.04233","month":"09","year":"2021","language":[{"iso":"eng"}],"external_id":{"arxiv":["2109.04233"]},"title":"A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness"},{"ec_funded":1,"date_published":"2021-08-03T00:00:00Z","year":"2021","doi":"10.48550/arXiv.2108.01733","month":"08","language":[{"iso":"eng"}],"external_id":{"arxiv":["2108.01733"]},"title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2108.01733"}],"article_number":"2108.01733","department":[{"_id":"JuFi"}],"date_created":"2021-09-13T12:17:11Z","related_material":{"record":[{"status":"public","id":"13043","relation":"later_version"},{"status":"public","id":"10007","relation":"dissertation_contains"}]},"type":"preprint","citation":{"chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2108.01733\">https://doi.org/10.48550/arXiv.2108.01733</a>.","apa":"Hensel, S., &#38; Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2108.01733\">https://doi.org/10.48550/arXiv.2108.01733</a>","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” <i>arXiv</i>. .","short":"S. Hensel, T. Laux, ArXiv (n.d.).","ista":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv, 2108.01733.","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2108.01733\">10.48550/arXiv.2108.01733</a>","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>ArXiv</i>, 2108.01733, doi:<a href=\"https://doi.org/10.48550/arXiv.2108.01733\">10.48550/arXiv.2108.01733</a>."},"day":"03","publication_status":"submitted","author":[{"first_name":"Sebastian","full_name":"Hensel, Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Tim","last_name":"Laux","full_name":"Laux, Tim"}],"status":"public","abstract":[{"text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.","lang":"eng"}],"article_processing_charge":"No","oa":1,"date_updated":"2023-09-07T13:30:45Z","publication":"arXiv","arxiv":1,"oa_version":"Preprint","project":[{"call_identifier":"H2020","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","_id":"10013"},{"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["530","532"],"related_material":{"record":[{"relation":"dissertation_contains","id":"10007","status":"public"}]},"ec_funded":1,"year":"2020","doi":"10.1007/s00205-019-01486-2","title":"Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension","external_id":{"isi":["000511060200001"]},"article_processing_charge":"Yes (via OA deal)","oa":1,"volume":236,"date_updated":"2023-09-07T13:30:45Z","project":[{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"oa_version":"Published Version","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["00039527"],"eissn":["14320673"]},"_id":"7489","citation":{"ama":"Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236:967-1087. doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>","mla":"Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:<a href=\"https://doi.org/10.1007/s00205-019-01486-2\">10.1007/s00205-019-01486-2</a>.","short":"J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236 (2020) 967–1087.","ista":"Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. 236, 967–1087.","ieee":"J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236. Springer Nature, pp. 967–1087, 2020.","apa":"Fischer, J. L., &#38; Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>","chicago":"Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-019-01486-2\">https://doi.org/10.1007/s00205-019-01486-2</a>."},"publication_status":"published","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","last_name":"Fischer"},{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","full_name":"Hensel, Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072"}],"abstract":[{"text":"In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.","lang":"eng"}],"department":[{"_id":"JuFi"}],"has_accepted_license":"1","file":[{"success":1,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"8779","file_name":"2020_ArchRatMechAn_Fischer.pdf","file_size":1897571,"date_created":"2020-11-20T09:14:22Z","checksum":"f107e21b58f5930876f47144be37cf6c","date_updated":"2020-11-20T09:14:22Z","access_level":"open_access"}],"date_created":"2020-02-16T23:00:50Z","article_type":"original","date_published":"2020-05-01T00:00:00Z","month":"05","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","file_date_updated":"2020-11-20T09:14:22Z","page":"967-1087","publication":"Archive for Rational Mechanics and Analysis","type":"journal_article","day":"01","status":"public","intvolume":"       236"},{"page":"251-297","issue":"3","publication":"Studia Mathematica","type":"journal_article","day":"01","status":"public","intvolume":"       252","department":[{"_id":"JuFi"},{"_id":"GradSch"}],"date_created":"2021-02-25T08:55:03Z","article_type":"original","date_published":"2020-03-01T00:00:00Z","month":"03","language":[{"iso":"eng"}],"publisher":"Instytut Matematyczny","scopus_import":"1","date_updated":"2023-10-17T09:15:53Z","volume":252,"article_processing_charge":"No","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","quality_controlled":"1","_id":"9196","publication_identifier":{"eissn":["1730-6337"],"issn":["0039-3223"]},"publication_status":"published","citation":{"mla":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” <i>Studia Mathematica</i>, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:<a href=\"https://doi.org/10.4064/sm180411-11-2\">10.4064/sm180411-11-2</a>.","ama":"Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. <i>Studia Mathematica</i>. 2020;252(3):251-297. doi:<a href=\"https://doi.org/10.4064/sm180411-11-2\">10.4064/sm180411-11-2</a>","short":"S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.","ista":"Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297.","ieee":"S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” <i>Studia Mathematica</i>, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020.","apa":"Hensel, S., &#38; Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. <i>Studia Mathematica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/sm180411-11-2\">https://doi.org/10.4064/sm180411-11-2</a>","chicago":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” <i>Studia Mathematica</i>. Instytut Matematyczny, 2020. <a href=\"https://doi.org/10.4064/sm180411-11-2\">https://doi.org/10.4064/sm180411-11-2</a>."},"keyword":["General Mathematics"],"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian"},{"last_name":"Rosati","full_name":"Rosati, Tommaso","first_name":"Tommaso"}],"abstract":[{"lang":"eng","text":"In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \\textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces."}],"isi":1,"year":"2020","doi":"10.4064/sm180411-11-2","external_id":{"isi":["000558100500002"],"arxiv":["1709.05202"]},"title":"Modelled distributions of Triebel–Lizorkin type"},{"type":"preprint","publication_status":"submitted","day":"11","citation":{"chicago":"Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” <i>ArXiv</i>, n.d.","ieee":"J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions,” <i>arXiv</i>. .","apa":"Fischer, J. L., Hensel, S., Laux, T., &#38; Simon, T. (n.d.). The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. <i>arXiv</i>.","ista":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv, 2003.05478.","short":"J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).","mla":"Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” <i>ArXiv</i>, 2003.05478.","ama":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. <i>arXiv</i>."},"author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","full_name":"Fischer, Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X"},{"orcid":"0000-0001-7252-8072","last_name":"Hensel","full_name":"Hensel, Sebastian","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Laux, Tim","last_name":"Laux","first_name":"Tim"},{"full_name":"Simon, Thilo","last_name":"Simon","first_name":"Thilo"}],"status":"public","abstract":[{"text":"We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a \"gradient flow calibration\" ensures that the route of steepest descent in the energy landscape is unique and stable.","lang":"eng"}],"oa":1,"date_updated":"2023-09-07T13:30:45Z","article_processing_charge":"No","arxiv":1,"publication":"arXiv","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","acknowledgement":"Parts of the paper were written during the visit of the authors to the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the framework of the trimester program “Evolution of Interfaces”. The support and the hospitality of HIM are gratefully acknowledged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 665385.","project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"oa_version":"Preprint","_id":"10012","date_published":"2020-03-11T00:00:00Z","ec_funded":1,"year":"2020","month":"03","language":[{"iso":"eng"}],"external_id":{"arxiv":["2003.05478"]},"title":"The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions","department":[{"_id":"JuFi"}],"article_number":"2003.05478","main_file_link":[{"url":"https://arxiv.org/abs/2003.05478","open_access":"1"}],"date_created":"2021-09-13T12:17:11Z","related_material":{"record":[{"id":"10007","relation":"dissertation_contains","status":"public"}]}}]