部分耗散的三维Boussinesq方程在静力平衡附近的稳定性和指数衰减  

Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation

作　　者：黎小丽 陈晓莉 Li Xiaoli;Chen Xiaoli(School of Mathematics and Statistics,Jiangxi Normal University,Nanchan 330022)

机构地区：[1]江西师范大学数学与统计学院,南昌330022

出　　处：《数学物理学报（A辑）》2023年第3期754-770,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971209,11961032);江西省教育厅基金资助~~。

摘　　要：该文研究了速度具有水平部分耗散而温度具有垂直耗散的三维Boussinesq方程在静力平衡附近的稳定性及大时间行为问题.在R^(2)×T上不仅建立了Boussinesq方程解的稳定性且该解有初值一样的对称性,还证明了速度和温度的振荡部分(u^(~),θ^(~))是指数衰减的.This paper is devoted to solving the stability and large time behavior problem on three dimensional Boussinesq equations with anisotropic dissipation and vertical thermal diffusion near the hydrostatic equilibrium.The stability of the solution with certain symmetries to the Boussinesq euations is established on the spatial domain R^(2)×T with the periodic box T=[−1/2,1/2].In addition,the oscillators of the velocity u and the temperatureθadmit the exponential decay in time variable t.

关 键 词：BOUSSINESQ方程 稳定性 静力平衡 大时间行为 

分 类 号：O175.27[理学—数学]