{"title":"间歇凸积分的Baire范畴法","authors":"G. Sattig, L. Székelyhidi","doi":"10.1007/s10474-023-01380-0","DOIUrl":null,"url":null,"abstract":"<div><p>We use a convex integration construction from [22] in a Baire\ncategory argument to show that weak solutions to the transport equation with\nincompressible vector fields with Sobolev regularity are generic in the Baire category\nsense. Using the construction of [7] we prove an analog statement for the\n3D Navier–Stokes equations.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Baire category method for intermittent convex integration\",\"authors\":\"G. Sattig, L. Székelyhidi\",\"doi\":\"10.1007/s10474-023-01380-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We use a convex integration construction from [22] in a Baire\\ncategory argument to show that weak solutions to the transport equation with\\nincompressible vector fields with Sobolev regularity are generic in the Baire category\\nsense. Using the construction of [7] we prove an analog statement for the\\n3D Navier–Stokes equations.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-023-01380-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01380-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Baire category method for intermittent convex integration
We use a convex integration construction from [22] in a Baire
category argument to show that weak solutions to the transport equation with
incompressible vector fields with Sobolev regularity are generic in the Baire category
sense. Using the construction of [7] we prove an analog statement for the
3D Navier–Stokes equations.
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