The Existence And Uniqueness Of Strong Solutions To The Initial-boundary Value Problem Of Three-dimensional Incompressible MHD Equations With Variable Magnetic Dissipation And Magnetic Diffusion Coefficient

Magnetohydrodynamics(MHD)is a subject that studies the interaction between electric and magnetic fields in conductive fluids on the basis of non-conducting fluid mechanics.It plays an important role in studying the motion properties of liquid metal,the mobility of ionized gas or plasma,etc.The basic equations of the MHD equations include electrodynamic equations and fluid mechanics equations.Among them,the electrodynamic equations include physical parameters,such as magnetic diffusion coefficient,resistivity and permeability.The fluid mechanics equations include magnetic dissipation coefficient,thermal conductivity rate,gas specific heat and other physical parameters.In L?(0,?;L2(?))xL?(0,?;H2(?))×L?(0,?;H2(?)),this paper deals with the initial boundary value problem of three-dimensional isentropic incompressible MHD equations with variable magnetic dissipation and magnetic diffusion coefficients in a bounded region?(?)R3 with smooth boundary.The initial boundary value problem of the linear equations corresponding to the non-linear MHD equations is studied by the iterative method.It's proved that there exists T*,0<T*<?,the initial boundary value problem of the linear MHD equations has a unique local strong solution in L?(0,T*;H2)by semidiscrete Galerkin method.When the initial value ?0,u0,b0 are sufficiently small and satisfy the natural compatibility condition,the iterative sequence {(?i,ui,bi)} of the strong solution to the initial boundary value problem of the linear MHD equations conver--ges to(?,u,b)in the norm of L?(0,+T*;L2)×L2(0,T*;H1)× L2(0,T*;H1).And(?,u,b)is the local strong solution of the initial boundary value problem of the nonlinear equations,and continuous with respect to time.Finally,by using the existence of the local strong solution of the initial boundary value problem of the nonlinear equations and the extension method,it's proved that there exists the unique global strong solution to the initial boundary value problem of the nonlinear equations.