[{"file":[{"relation":"main_file","access_level":"open_access","success":1,"file_id":"9270","creator":"dernst","date_created":"2021-03-22T08:31:29Z","checksum":"23449e44dc5132501a5c86e70638800f","file_size":558006,"date_updated":"2021-03-22T08:31:29Z","content_type":"application/pdf","file_name":"2021_ArchRationalMechAnal_Leopold.pdf"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["00039527"],"eissn":["14320673"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2021-02-26T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"month":"02","publication":"Archive for Rational Mechanics and Analysis","has_accepted_license":"1","volume":240,"acknowledgement":"Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron.","ddc":["510"],"doi":"10.1007/s00205-021-01616-9","arxiv":1,"day":"26","abstract":[{"lang":"eng","text":"We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order."}],"date_updated":"2023-08-07T14:12:27Z","citation":{"chicago":"Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>.","ieee":"N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240. Springer Nature, pp. 383–417, 2021.","ama":"Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. 2021;240:383-417. doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>","apa":"Leopold, N. K., Mitrouskas, D. J., &#38; Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01616-9\">https://doi.org/10.1007/s00205-021-01616-9</a>","ista":"Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.","short":"N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417.","mla":"Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 240, Springer Nature, 2021, pp. 383–417, doi:<a href=\"https://doi.org/10.1007/s00205-021-01616-9\">10.1007/s00205-021-01616-9</a>."},"year":"2021","isi":1,"external_id":{"arxiv":["2001.03993"],"isi":["000622226200001"]},"publisher":"Springer Nature","article_type":"original","page":"383-417","ec_funded":1,"quality_controlled":"1","file_date_updated":"2021-03-22T08:31:29Z","publication_status":"published","article_processing_charge":"No","date_created":"2021-03-14T23:01:34Z","department":[{"_id":"RoSe"}],"title":"Derivation of the Landau–Pekar equations in a many-body mean-field limit","intvolume":"       240","_id":"9246","scopus_import":"1","author":[{"last_name":"Leopold","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mitrouskas, David Johannes","last_name":"Mitrouskas","first_name":"David Johannes","id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d"},{"first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}]},{"has_accepted_license":"1","publication":"Archive for Rational Mechanics and Analysis","month":"05","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2020-05-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["14320673"],"issn":["00039527"]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"record":[{"id":"10007","relation":"dissertation_contains","status":"public"}]},"file":[{"date_updated":"2020-11-20T09:14:22Z","content_type":"application/pdf","file_name":"2020_ArchRatMechAn_Fischer.pdf","date_created":"2020-11-20T09:14:22Z","file_size":1897571,"checksum":"f107e21b58f5930876f47144be37cf6c","file_id":"8779","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access"}],"author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","first_name":"Sebastian","last_name":"Hensel"}],"scopus_import":"1","_id":"7489","intvolume":"       236","title":"Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JuFi"}],"date_created":"2020-02-16T23:00:50Z","publication_status":"published","file_date_updated":"2020-11-20T09:14:22Z","quality_controlled":"1","ec_funded":1,"page":"967-1087","article_type":"original","publisher":"Springer Nature","external_id":{"isi":["000511060200001"]},"isi":1,"citation":{"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.","short":"J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236 (2020) 967–1087.","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>.","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.","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>.","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>","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>"},"year":"2020","date_updated":"2023-09-07T13:30:45Z","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"}],"day":"01","doi":"10.1007/s00205-019-01486-2","ddc":["530","532"],"volume":236}]