Tim Binz , Matthias Hieber , Amru Hussein , Martin Saal
{"title":"The primitive equations with stochastic wind driven boundary conditions","authors":"Tim Binz , Matthias Hieber , Amru Hussein , Martin Saal","doi":"10.1016/j.matpur.2024.01.001","DOIUrl":null,"url":null,"abstract":"<div><p>The primitive equations for geophysical flows are studied under the influence of <em>stochastic wind driven boundary conditions</em> modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span>-<span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>z</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi><mi>y</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-setting. This solution is constructed in critical spaces.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"183 ","pages":"Pages 76-101"},"PeriodicalIF":2.1000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000072/pdfft?md5=30fb9d977114954181c690ca0fa1ea9e&pid=1-s2.0-S0021782424000072-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de Mathematiques Pures et Appliquees","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000072","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The primitive equations for geophysical flows are studied under the influence of stochastic wind driven boundary conditions modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic --setting. This solution is constructed in critical spaces.
期刊介绍:
Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.