{"title":"A regularity criterion for the 3D axisymmetric Boussinesq equations with non-zero swirl","authors":"Peng Wang, Zhengguang Guo","doi":"10.1063/5.0125404","DOIUrl":null,"url":null,"abstract":"In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ > 0, if the angular component of velocity field uθ(t, r, z) satisfies sup0<t<T‖zuθ‖L∞(Ωδ)≤ϵ, where Ωδ≔x1,x2,z∈R3|x12+x22<δ denotes a thin cylinder with infinite height and radius δ > 0, which is independent of the initial data, then the weak solution (u, ρ) to 3D Boussinesq equations is regular in (0, T].","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"30 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0125404","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ > 0, if the angular component of velocity field uθ(t, r, z) satisfies sup0 0, which is independent of the initial data, then the weak solution (u, ρ) to 3D Boussinesq equations is regular in (0, T].
期刊介绍：
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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