{"title":"Asymptotic stability to semi-stationary Boussinesq equations without thermal conduction","authors":"Jianguo Li","doi":"10.1063/5.0150791","DOIUrl":null,"url":null,"abstract":"We study the stability problem of steady solutions to the semi-stationary Boussinesq equations in the strip domain R2×(0,1). For an equilibrium state with any general steady solution θe which satisfies ϑe > m > 0, we show the global existence and asymptotic behavior of solutions to the system with the no-slip boundary condition when the initial temperature is close enough to it. Thus such a steady solution is asymptotically stable, which reflects the well-known phenomenon of Rayleigh-Taylor stability.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0150791","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We study the stability problem of steady solutions to the semi-stationary Boussinesq equations in the strip domain R2×(0,1). For an equilibrium state with any general steady solution θe which satisfies ϑe > m > 0, we show the global existence and asymptotic behavior of solutions to the system with the no-slip boundary condition when the initial temperature is close enough to it. Thus such a steady solution is asymptotically stable, which reflects the well-known phenomenon of Rayleigh-Taylor stability.
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