Boussinesq方程稳态解的存在性与正则性  

Existence and Regularity of Steady-state Solutions of Boussinesq Equations

作　　者：张敏心 陈敏 罗宏 ZHANG Minxin;CHEN Min;LUO Hong(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2024年第1期48-54,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省科技厅应用基础项目(22CXTD0029)。

摘　　要：研究二维Boussinesq方程稳态解的存在性与正则性.首先,利用弱连续算子锐角原理得到方程弱解存在性的条件.其次,利用ADN理论、线性椭圆理论和迭代方法证明方程强解的存在性.最后,利用Sard-Smale定理得到解的有限性,并通过ADN理论和线性椭圆方程理论研究方程古典解的存在性.In this paper,the existence and regularity of steady-state solutions of 2D Boussinesq equations are studied.Firstly,the existence condition for weak solutions of the equations is obtained by acute angle principle of weakly continuous operator.Secondly,ADN theory,the theory of the linear elliptic equation and the iterative method are used to prove the existence of strong solutions.In addition,the finiteness of the solutions is obtained by Sard-Smale theorem,while the existence of classical solutions of the equations is investigated by ADN theory and the theory for the linear elliptic equation.

关 键 词：稳态解 存在性 正则性 有限性 

分 类 号：O175.29[理学—数学]