THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE  

作　　者：Saiguo XU Zhong TAN 徐赛国;谭忠(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China;Shenzhen Research Institute of Xiamen University,Shenzhen 518057,China)

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China [3]Shenzhen Research Institute of Xiamen University,Shenzhen 518057,China

出　　处：《Acta Mathematica Scientia》2024年第4期1466-1486,共21页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(12071391,12231016);the Guangdong Basic and Applied Basic Research Foundation(2022A1515010860)。

摘　　要：This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).

关 键 词：Boussinesq equations partial dissipation stability DECAY 

分 类 号：O175[理学—数学]