关于Boussinesq方程组无粘极限的研究

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 91-99.

关于Boussinesq方程组无粘极限的研究

郭连红()

广州番禺职业技术学院公共课教学部广州 511483

收稿日期:2020-01-07 出版日期:2021-02-26 发布日期:2021-01-29
作者简介:郭连红, E-mail: guoat164@163.com
基金资助:
广东普通高校重点科研（自然科学）(2019KZDXM042)

Research on the Inviscid Limit for Boussinesq Equations

Lianhong Guo()

Public Course Teaching Department, Guangzhou Panyu Polytechnic, Guangzhou 511483

Received:2020-01-07 Online:2021-02-26 Published:2021-01-29
Supported by:
the Guangdong Key Research in Common Colleges and Universities (Natural Science)(2019KZDXM042)

摘要/Abstract

摘要：

该文主要研究三维Boussinesq方程组的无粘极限问题.为了克服Boussinesq方程组中温度和速度耦合项产生的困难，带温度的涡量方程需要与Slip边界条件匹配，通过计算得到温度更高阶的边界条件，结合迹定理和能量估计，最后得到了三维粘性Boussinesq方程组初边值问题强解的存在唯一性，并在平坦区域上得到了强解的收敛率.

关键词: Boussinesq方程组, Slip边界条件, 无粘极限

Abstract:

In this paper, we investigate the inviscid limit of the 3D viscous Boussinesq equations with slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary value problems for such systems. Furthermore, we establish the vanishing viscosity limit process and obtain a strong rate of convergence as the boundary of the domain is flat. In addition, the key observation is that the boundary term as $θ$ can be estimated by the part of high order of energy through the trace formula.

Key words: Boussinesq equations, Vanishing viscosity limit, Slip boundary conditions

中图分类号:

O175.2

郭连红. 关于Boussinesq方程组无粘极限的研究[J]. 数学物理学报, 2021, 41(1): 91-99.

Lianhong Guo. Research on the Inviscid Limit for Boussinesq Equations[J]. Acta mathematica scientia,Series A, 2021, 41(1): 91-99.

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