THE ZERO LIMIT OF THERMAL DIFFUSIVITY FOR THE 2D DENSITY-DEPENDENT BOUSSINESQ EQUATIONS  

作　　者：叶霞 徐艳霞 王泽佳 Xia YE;Yanxia XU;Zejia WANG(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China

出　　处：《Acta Mathematica Scientia》2023年第4期1800-1818,共19页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation of China(12061037,11971209);the Natural Science Foundation of Jiangxi Province(20212BAB201016);National Natural Science Foundation of China(11861038)。

摘　　要：This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.

关 键 词：density-dependent Boussinesq equation zero thermal diffusivity convergence rate boundary layer 

分 类 号：O175[理学—数学]