{"title":"On the Regularity of the Solution for Incompressible 3D Navier–Stokes Equation with Periodic Boundary Conditions","authors":"Qun Lin","doi":"10.1134/S1061920824020092","DOIUrl":null,"url":null,"abstract":"<p> In this paper, we prove that the vorticity belongs to <span>\\(L^{\\infty}(0,T;L^2(\\Omega))\\)</span> for 3D incompressible Navier–Stokes equation with space-periodic boundary conditions, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary systems to approximate the original system of vorticity equation. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"255 - 275"},"PeriodicalIF":1.7000,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824020092","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove that the vorticity belongs to \(L^{\infty}(0,T;L^2(\Omega))\) for 3D incompressible Navier–Stokes equation with space-periodic boundary conditions, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary systems to approximate the original system of vorticity equation.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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