三维Boussinesq-MHD方程在Navier-slip边界条件下解的存在性  

Existence of Solutions for the 3D Boussinesq-MHD Equations with Navier-slip Boundary Conditions

作　　者：张诗语 李俐玫 朱芷逸 ZHANG Shiyu;LI Limei;ZHU Zhiyi(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan;V.C.&V.R.Key Lab.of Sichuan Province,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 [2]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2023年第5期601-607,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11701399)。

摘　　要：研究在光滑有界区域Ω中带Navier-slip边界条件的三维不可压缩Boussinesq-MHD方程组解的存在性问题.首先,运用Galerkin近似法得到方程组弱解的全局存在性.其次在H1范数意义下,通过能量估计得到关于近似解的一致先验估计,再结合标准的极限过程、Gronwall不等式以及初始条件等证明该方程组强解的局部存在唯一性.We investigate the existence of solutions for the 3D incompressible Boussinesq-MHD equations with the Navier-slip boundary conditions in a smooth bounded domain.Firstly,the global existence of weak solution is obtained by Galerkin approximation.Secondly,the uniform prior estimates of the approximate solution is obtained by using the energy estimation method in the sense of H1 norm.Then combining with the standard limit process,Gronwall inequality and initial conditions,the local existence and uniqueness of the strong solution of the system are proved.

关 键 词：Boussinesq-MHD方程 Navier-slip边界条件 Galerkin近似 弱解 强解 

分 类 号：O175.29[理学—数学]