{"title":"On Isolated Singularities for the Stationary Navier–Stokes System","authors":"Alfonsina Tartaglione","doi":"10.1007/s00021-024-00905-z","DOIUrl":null,"url":null,"abstract":"<div><p>The classical problem of removable singularities is considered for solutions to the stationary Navier–Stokes system in dimension <span>\\(n\\ge 3\\)</span> and an old theorem of Shapiro (TAMS 187:335–363, 1974) is recovered and extended to solutions in a half ball vanishing on the flat boundary. Moreover, for <span>\\(n=4\\)</span> it is proved that there are not distributional solutions, smooth away from the singularity and such that <span>\\(u(x)=O(|x|^{-1})\\)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00905-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00905-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The classical problem of removable singularities is considered for solutions to the stationary Navier–Stokes system in dimension \(n\ge 3\) and an old theorem of Shapiro (TAMS 187:335–363, 1974) is recovered and extended to solutions in a half ball vanishing on the flat boundary. Moreover, for \(n=4\) it is proved that there are not distributional solutions, smooth away from the singularity and such that \(u(x)=O(|x|^{-1})\).
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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