[{"publication":"Stochastics and Partial Differential Equations: Analysis and Computations","page":"1254–1378","file_date_updated":"2023-08-14T11:51:04Z","intvolume":"        11","status":"public","day":"01","type":"journal_article","date_created":"2021-10-23T10:50:22Z","file":[{"file_size":1635193,"file_name":"2023_StochPartialDiffEquations_Clozeau.pdf","checksum":"f83dcaecdbd3ace862c4ed97a20e8501","date_created":"2023-08-14T11:51:04Z","access_level":"open_access","date_updated":"2023-08-14T11:51:04Z","success":1,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"14052"}],"has_accepted_license":"1","department":[{"_id":"JuFi"}],"scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"09","article_type":"original","date_published":"2023-09-01T00:00:00Z","publication_identifier":{"issn":["2194-0401"]},"_id":"10173","quality_controlled":"1","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","arxiv":1,"article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-14T11:51:47Z","oa":1,"volume":11,"abstract":[{"text":"We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods.","lang":"eng"}],"author":[{"first_name":"Nicolas","last_name":"Clozeau","full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b"}],"citation":{"chicago":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s40072-022-00254-w\">https://doi.org/10.1007/s40072-022-00254-w</a>.","ieee":"N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 11. Springer Nature, pp. 1254–1378, 2023.","apa":"Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-022-00254-w\">https://doi.org/10.1007/s40072-022-00254-w</a>","ista":"Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.","short":"N. Clozeau, Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) 1254–1378.","ama":"Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2023;11:1254–1378. doi:<a href=\"https://doi.org/10.1007/s40072-022-00254-w\">10.1007/s40072-022-00254-w</a>","mla":"Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:<a href=\"https://doi.org/10.1007/s40072-022-00254-w\">10.1007/s40072-022-00254-w</a>."},"publication_status":"published","ddc":["510"],"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,"external_id":{"arxiv":["2102.07452"],"isi":["000799715600001"]},"title":"Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields","doi":"10.1007/s40072-022-00254-w","year":"2023"},{"date_created":"2023-02-02T10:45:47Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","date_published":"2023-11-28T00:00:00Z","article_type":"original","month":"11","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","status":"public","type":"journal_article","day":"28","ddc":["510"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40072-023-00319-4"}],"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":{"arxiv":["2207.08293"]},"title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","ec_funded":1,"doi":"10.1007/s40072-023-00319-4","year":"2023","acknowledgement":"The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti for her support in creating the picture. The author\r\nthanks the anonymous referee for helpful comments. ","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"oa_version":"Submitted Version","_id":"12486","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"date_updated":"2023-12-18T07:53:45Z","oa":1,"article_processing_charge":"No","arxiv":1,"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","first_name":"Antonio"}],"abstract":[{"text":"This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas.","lang":"eng"}],"publication_status":"epub_ahead","citation":{"chicago":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s40072-023-00319-4\">https://doi.org/10.1007/s40072-023-00319-4</a>.","apa":"Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-023-00319-4\">https://doi.org/10.1007/s40072-023-00319-4</a>","ieee":"A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2023.","ista":"Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.","short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations (2023).","mla":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">10.1007/s40072-023-00319-4</a>.","ama":"Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">10.1007/s40072-023-00319-4</a>"}},{"department":[{"_id":"JuFi"}],"date_created":"2023-01-12T12:12:29Z","date_published":"2022-10-27T00:00:00Z","article_type":"original","month":"10","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","type":"journal_article","day":"27","status":"public","isi":1,"main_file_link":[{"url":"https://doi.org/10.1007/s40072-022-00277-3","open_access":"1"}],"doi":"10.1007/s40072-022-00277-3","year":"2022","external_id":{"isi":["000874389000001"]},"title":"The stochastic primitive equations with transport noise and turbulent pressure","oa":1,"date_updated":"2023-08-16T09:11:38Z","article_processing_charge":"Yes (via OA deal)","acknowledgement":"The authors thank the anonymous referees for their helpful comments and suggestions. Open Access funding enabled and organized by Projekt DEAL.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Published Version","_id":"12178","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"publication_status":"epub_ahead","citation":{"short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential Equations: Analysis and Computations (2022).","ista":"Agresti A, Hieber M, Hussein A, Saal M. 2022. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations.","ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2022. doi:<a href=\"https://doi.org/10.1007/s40072-022-00277-3\">10.1007/s40072-022-00277-3</a>","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s40072-022-00277-3\">10.1007/s40072-022-00277-3</a>.","chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40072-022-00277-3\">https://doi.org/10.1007/s40072-022-00277-3</a>.","apa":"Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2022). The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-022-00277-3\">https://doi.org/10.1007/s40072-022-00277-3</a>","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with transport noise and turbulent pressure,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2022."},"author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","full_name":"Agresti, Antonio","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"first_name":"Matthias","last_name":"Hieber","full_name":"Hieber, Matthias"},{"first_name":"Amru","last_name":"Hussein","full_name":"Hussein, Amru"},{"full_name":"Saal, Martin","last_name":"Saal","first_name":"Martin"}],"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"abstract":[{"text":"In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.","lang":"eng"}]},{"file":[{"file_id":"9309","creator":"dernst","relation":"main_file","content_type":"application/pdf","success":1,"access_level":"open_access","date_updated":"2021-04-06T09:31:28Z","checksum":"6529b609c9209861720ffa4685111bc6","date_created":"2021-04-06T09:31:28Z","file_size":727005,"file_name":"2021_StochPartDiffEquation_Hensel.pdf"}],"date_created":"2021-04-04T22:01:21Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"month":"03","date_published":"2021-03-21T00:00:00Z","article_type":"original","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","file_date_updated":"2021-04-06T09:31:28Z","page":"892–939","intvolume":"         9","status":"public","day":"21","type":"journal_article","ddc":["510"],"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,"external_id":{"isi":["000631001700001"]},"title":"Finite time extinction for the 1D stochastic porous medium equation with transport noise","doi":"10.1007/s40072-021-00188-9","year":"2021","ec_funded":1,"_id":"9307","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","project":[{"grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program"}],"quality_controlled":"1","oa_version":"Published Version","date_updated":"2023-08-07T14:31:59Z","volume":9,"oa":1,"article_processing_charge":"Yes (via OA deal)","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"}],"author":[{"orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","last_name":"Hensel","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","citation":{"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>.","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.","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>","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.","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>."}}]