Existence Of Solutions And Inviscid Limit For The Three-dimensional Boussinesq Equations For MHD Convection

In this thesis,we study the Cauchy problem and the vanishing viscosity limit for the 3D MHD coupling Boussinesq equations with slip boundary conditions.Slip boundary condition is a commonly used condition,which means that there is a stagnant layer of fluid close to the wall allowing a fluid to slip,and the slip velocity is proportional to the shear stress.In this thesis,temperature has Neumann boundary conditions,speed field and magnetic field has slip boundary conditions.Firstly,we use the Galerkin method,Sobolev inequalities,Gronwall inequality and energy estimates to prove the existence of global weak solutions and local existence and uniqueness of strong solutions for the system.Secondly,when the boundary of the region is flat,we get the convergence rate of the system by using the uniformly estimation results in this thesis.