{"title":"The time periodic problem for the Navier-Stokes equations on half spaces with moving boundary: Linear theory","authors":"","doi":"10.1016/j.jde.2024.07.046","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, we develop a linear theory to deal with the time periodic problem for the Navier-Stokes equations on unbounded domains with moving boundary. Compared to the case of bounded domains the underlying modified time-dependent Stokes operators are no longer invertible, thus leading to a more sophisticated construction of the evolution operator. Moreover, Sobolev embeddings on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> spaces imply restrictions on <em>q</em> depending on geometric properties of the domain. The theory is focusing on the half space case, the construction and local-in-time estimates of the evolution operator and its adjoint in view of time periodic solutions.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-08-16","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/S0022039624004753","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 article, we develop a linear theory to deal with the time periodic problem for the Navier-Stokes equations on unbounded domains with moving boundary. Compared to the case of bounded domains the underlying modified time-dependent Stokes operators are no longer invertible, thus leading to a more sophisticated construction of the evolution operator. Moreover, Sobolev embeddings on spaces imply restrictions on q depending on geometric properties of the domain. The theory is focusing on the half space case, the construction and local-in-time estimates of the evolution operator and its adjoint in view of time periodic solutions.
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