MHD对流三维Boussinesq方程组解的存在性  

Existence of solutions of MHD convection 3D Boussinesq equations

作　　者：朱芷逸 李俐玫 张诗语 ZHU Zhi-yi;LI Li-mei;ZHANG Shi-yu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,Sichuan,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068

出　　处：《西北师范大学学报（自然科学版）》2022年第4期22-27,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11701399)。

摘　　要：在有界区域中研究了三维磁流体方程组(MHD)耦合Boussinesq方程初边值问题,其中速度u和磁场H具有Slip边界条件,温度具有Neumann边界条件,Slip边界条件在靠近壁面处有一个流体滞留层允许流体滑动,滑移速度与剪应力成正比.应用Galerkin方法、Sobolev不等式、Gronwall不等式,并结合能量估计证明了该方程组全局弱解的存在性和强解的局部存在唯一性.The Cauchy problem is discussed for the 3D MHD coupling Boussinesq equations,where velocity field and magnetic field have Slip boundary conditions,temperature has Neumann boundary conditions.Slip boundary condition means that there is a stagnant layer of fluid close to the wall allowing a fluid to slip.In this paper,the Galerkin method,Sobolev inequalities,Gronwall inequality and energy estimates are used to prove the existence of global weak solutions as well as local existence and uniqueness of strong solutions for the system.

关 键 词：三维磁流体 BOUSSINESQ方程 弱解 强解 Slip边界条件 

分 类 号：O175.29[理学—数学]