{"title":"Asymptotic behavior for stationary Navier-Stokes equations","authors":"Yupei Li, Wei Luo","doi":"10.1016/j.jde.2024.10.011","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the asymptotic behavior of solutions to the axisymmetric stationary Navier-Stokes equations. We assume that the flow is periodic in <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>-direction and has no swirl. Under the general integrability condition, we prove the pointwise decay estimate of the vorticity <em>ω</em> and obtain the Liouville-type theorem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624006624","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the asymptotic behavior of solutions to the axisymmetric stationary Navier-Stokes equations. We assume that the flow is periodic in -direction and has no swirl. Under the general integrability condition, we prove the pointwise decay estimate of the vorticity ω and obtain the Liouville-type theorem.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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