{"title":"无热传导半稳态布森斯克方程的渐近稳定性","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":"{\"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}","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
摘要
我们研究了带状域R2×(0,1)中半稳态布森斯克方程稳态解的稳定性问题。对于具有满足 ϑe > m > 0 的任意一般稳定解θe 的平衡态,我们证明了当初始温度足够接近无滑动边界条件时,系统解的全局存在性和渐近行为。因此,这种稳定解是渐近稳定的,这反映了著名的瑞利-泰勒稳定性现象。
Asymptotic stability to semi-stationary Boussinesq equations without thermal conduction
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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