{"title":"斯托克斯算子在有界和外部 $$C^1$$ 域中的残差估计值","authors":"Jun Geng, Zhongwei Shen","doi":"10.1007/s00208-024-02956-z","DOIUrl":null,"url":null,"abstract":"<p>We establish resolvent estimates in <span>\\(L^q\\)</span> spaces for the Stokes operator in a bounded <span>\\(C^1\\)</span> domain <span>\\(\\Omega \\)</span> in <span>\\(\\mathbb {R}^{d}\\)</span>. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in <span>\\(L^q(\\Omega ; \\mathbb {C}^d)\\)</span> for any <span>\\(1< q< \\infty \\)</span> and <span>\\(d\\ge 2\\)</span>. The case of an exterior <span>\\(C^1\\)</span> domain is also studied.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains\",\"authors\":\"Jun Geng, Zhongwei Shen\",\"doi\":\"10.1007/s00208-024-02956-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish resolvent estimates in <span>\\\\(L^q\\\\)</span> spaces for the Stokes operator in a bounded <span>\\\\(C^1\\\\)</span> domain <span>\\\\(\\\\Omega \\\\)</span> in <span>\\\\(\\\\mathbb {R}^{d}\\\\)</span>. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in <span>\\\\(L^q(\\\\Omega ; \\\\mathbb {C}^d)\\\\)</span> for any <span>\\\\(1< q< \\\\infty \\\\)</span> and <span>\\\\(d\\\\ge 2\\\\)</span>. The case of an exterior <span>\\\\(C^1\\\\)</span> domain is also studied.</p>\",\"PeriodicalId\":18304,\"journal\":{\"name\":\"Mathematische Annalen\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Annalen\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00208-024-02956-z\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02956-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains
We establish resolvent estimates in \(L^q\) spaces for the Stokes operator in a bounded \(C^1\) domain \(\Omega \) in \(\mathbb {R}^{d}\). As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in \(L^q(\Omega ; \mathbb {C}^d)\) for any \(1< q< \infty \) and \(d\ge 2\). The case of an exterior \(C^1\) domain is also studied.
期刊介绍:
Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin.
The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin.
Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.