{"title":"轴对称纳维-斯托克斯方程的精细大时间渐近线","authors":"Christian Seis, Dominik Winkler","doi":"10.1007/s00028-024-01001-5","DOIUrl":null,"url":null,"abstract":"<p>We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in <span>\\({\\mathbb {R}}^3\\)</span>. We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard <span>\\(L^2\\)</span>-based entropy methods.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fine large-time asymptotics for the axisymmetric Navier–Stokes equations\",\"authors\":\"Christian Seis, Dominik Winkler\",\"doi\":\"10.1007/s00028-024-01001-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in <span>\\\\({\\\\mathbb {R}}^3\\\\)</span>. We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard <span>\\\\(L^2\\\\)</span>-based entropy methods.</p>\",\"PeriodicalId\":51083,\"journal\":{\"name\":\"Journal of Evolution Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Evolution Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00028-024-01001-5\",\"RegionNum\":3,\"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":"Journal of Evolution Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00028-024-01001-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fine large-time asymptotics for the axisymmetric Navier–Stokes equations
We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in \({\mathbb {R}}^3\). We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard \(L^2\)-based entropy methods.
期刊介绍：
The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications.
Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field.
Particular topics covered by the journal are:
Linear and Nonlinear Semigroups
Parabolic and Hyperbolic Partial Differential Equations
Reaction Diffusion Equations
Deterministic and Stochastic Control Systems
Transport and Population Equations
Volterra Equations
Delay Equations
Stochastic Processes and Dirichlet Forms
Maximal Regularity and Functional Calculi
Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations
Evolution Equations in Mathematical Physics
Elliptic Operators
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