The Zero Limit of Thermal Diffusivity for the 2D Density-Dependent Boussinesq Equations

被引：0

作者：

Ye, Xia ^{[1
]}

Xu, Yanxia ^{[1
]}

Wang, Zejia ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Sch Math & Stat, Nanchang, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 04期

基金：

中国国家自然科学基金;

关键词：

density-dependent Boussinesq equation; zero thermal diffusivity; convergence rate; boundary layer; GLOBAL WELL-POSEDNESS; REGULARITY;

D O I：

10.1007/s10473-023-0420-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 value & delta;(k) = k(& alpha;) with any & alpha; & ISIN; (0, 1/4) for a small diffusivity coefficient k > 0, and we also find a function to describe the properties of the boundary layer.

引用

页码：1800 / 1818

页数：19