首页|THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE
THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE
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万方数据
维普
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 atmo-spheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R2,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 temperature θ into the horizontal average(ū,(θ))and the corresponding oscilla-tion((u),(θ)),we can derive the global stability in H2 and the exponential decay of(ũ,(θ))to zero in H1.Moreover,we also obtain that(ū2,(θ))decays exponentially to zero in H1,and that ū1 decays exponentially to ū1(∞)in H1 as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H3 for the 3D case R3.
万方数据
维普
