{"title":"Stokes Resolvent Estimates in Spaces of Bounded Functions","authors":"K. Abe, Y. Giga, Matthias Hieber","doi":"10.24033/ASENS.2251","DOIUrl":null,"url":null,"abstract":"We give a direct proof for the analyticity of the Stokes semigroup in spaces of bounded functions. This was recently proved by an indirect argument by the first and second authors for a class of domains called strictly admissible domains including bounded and exterior domains. Invoking the strictly admissibility, our approach is based on an adjustment of a standard resolvent estimate method for general elliptic operators introduced by K. Masuda (1972) and H. B. Stewart (1974). The resolvent approach in particular clarifies the sectorial region, Re z > 0 for z ∈ C for which the Stokes semigroup has an analytic continuation in spaces of bounded functions.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"8 1","pages":"537-559"},"PeriodicalIF":1.3000,"publicationDate":"2012-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"51","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2251","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 51
Abstract
We give a direct proof for the analyticity of the Stokes semigroup in spaces of bounded functions. This was recently proved by an indirect argument by the first and second authors for a class of domains called strictly admissible domains including bounded and exterior domains. Invoking the strictly admissibility, our approach is based on an adjustment of a standard resolvent estimate method for general elliptic operators introduced by K. Masuda (1972) and H. B. Stewart (1974). The resolvent approach in particular clarifies the sectorial region, Re z > 0 for z ∈ C for which the Stokes semigroup has an analytic continuation in spaces of bounded functions.
给出了有界函数空间中Stokes半群的可解析性的一个直接证明。最近，第一和第二作者通过间接论证证明了这一点，证明了一类称为严格可容许域的域包括有界域和外域。引用严格容许性，我们的方法是基于K. Masuda(1972)和H. B. Stewart(1974)引入的一般椭圆算子的标准解析估计方法的调整。特别地，解解法澄清了对于z∈C, Stokes半群在有界函数空间中具有解析延拓的扇形区域Re z > 0。
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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