{"article_processing_charge":"No","abstract":[{"text":"In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. Moreover, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equations, tamed Navier-Stokes equations, and Allen-Cahn equation.","lang":"eng"}],"status":"public","publication_status":"epub_ahead","publisher":"Springer Nature","date_published":"2024-02-02T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"date_created":"2023-02-02T10:45:15Z","oa_version":"Preprint","title":"The critical variational setting for stochastic evolution equations","month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2206.00230"]},"publication":"Probability Theory and Related Fields","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","first_name":"Antonio","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","last_name":"Agresti"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"scopus_import":"1","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"_id":"12485","year":"2024","main_file_link":[{"url":"https://doi.org/10.1007/s00440-023-01249-x","open_access":"1"}],"article_type":"original","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"oa":1,"ec_funded":1,"department":[{"_id":"JuFi"}],"doi":"10.1007/s00440-023-01249-x","date_updated":"2024-02-26T09:39:07Z","citation":{"mla":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>.","ista":"Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields.","chicago":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>.","ieee":"A. Agresti and M. Veraar, “The critical variational setting for stochastic evolution equations,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024.","ama":"Agresti A, Veraar M. The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>","apa":"Agresti, A., &#38; Veraar, M. (2024). The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>","short":"A. Agresti, M. Veraar, Probability Theory and Related Fields (2024)."},"quality_controlled":"1","day":"02","acknowledgement":"The first 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) . The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO)."}