{"title":"含传输噪声的随机二维Euler方程的适定性。","authors":"Oana Lang, Dan Crisan","doi":"10.1007/s40072-021-00233-7","DOIUrl":null,"url":null,"abstract":"<p><p>We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.</p>","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"11 2","pages":"433-480"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10185632/pdf/","citationCount":"24","resultStr":"{\"title\":\"Well-posedness for a stochastic 2D Euler equation with transport noise.\",\"authors\":\"Oana Lang, Dan Crisan\",\"doi\":\"10.1007/s40072-021-00233-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.</p>\",\"PeriodicalId\":74872,\"journal\":{\"name\":\"Stochastic partial differential equations : analysis and computations\",\"volume\":\"11 2\",\"pages\":\"433-480\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10185632/pdf/\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastic partial differential equations : analysis and computations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40072-021-00233-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2022/1/29 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic partial differential equations : analysis and computations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40072-021-00233-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/1/29 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
Well-posedness for a stochastic 2D Euler equation with transport noise.
We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.
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