{"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":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01380-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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