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

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 754-770.

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

黎小丽(),陈晓莉()

江西师范大学数学与统计学院南昌 330022

收稿日期:2022-06-29 修回日期:2023-02-06 出版日期:2023-06-26 发布日期:2023-06-01
作者简介:黎小丽,E-mail:Lixli629@163.com;|陈晓莉,E-mail:littleli_chen@163.com
基金资助:
国家自然科学基金(11971209);国家自然科学基金(11961032);江西省教育厅基金

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

Li Xiaoli(),Chen Xiaoli()

School of Mathematics and Statistics, Jiangxi Normal University, Nanchan 330022

Received:2022-06-29 Revised:2023-02-06 Online:2023-06-26 Published:2023-06-01
Supported by:
NSFC(11971209);NSFC(11961032);Foundation of Jiangxi Teacher's Division

摘要/Abstract

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$R^2\times T$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$(\tilde{u},\tilde{\theta})$是指数衰减的.

关键词: Boussinesq方程, 稳定性, 静力平衡, 大时间行为

Abstract:

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 $R^2\times \mathrm{T}$ with the periodic box $\mathrm{T}=[-\frac12,\frac12]$. In addition, the oscillators of the velocity $u$ and the temperature $\theta$ admit the exponential decay in time variable $t$.

Key words: Boussinesq equations, Stability, Hydrostatic equilibrium, Large-time behavior

中图分类号:

O175.27

黎小丽,陈晓莉. 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[J]. 数学物理学报, 2023, 43(3): 754-770.

Li Xiaoli,Chen Xiaoli. Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation[J]. Acta mathematica scientia,Series A, 2023, 43(3): 754-770.

参考文献 13

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