Viscosity And Resistivity Coefficients Are Well-posed For Local Strong Solutions Of Density-dependent Three-dimensional Incompressible Magnetohydrodynamic Equations

Magnetohydrodynamics(MHD)studies the motion of conductive fluid in electromagnetic field.MHD equations are the basic equations of MHD,which are coupled by Navier Stokes equations and Maxwell equations.In this paper,we study the system of the three-dimensional incompressible magnetohydrodynamics equations with viscosity and resistivity coefficients dependent on density,and the well posedness of local strong solutions for the initial boundary value problem of the equations is studied.Firstly,we study the initial boundary value problem of the approximate equations of MHD equations by employing the mollifier method.It is proved that the approximate equations have a unique solution in C?(?R×[0,?))when the initial value satisfies 0<(?)?0??0??,??h0??,v??0?v,u0,H0?C0,?? ?R),and by using the prior estimation of solutions,the existence theorem of solutions and the compactness theory of function space,it is certified that there is a unique local strong solution for the initial boundary value problem of MHD equations.Finally,it is demonstrated that the local strong solution continuously depends on the initial data when the initial value satisfies the ?0?0,?0?L3/2?L??H1,?(?0)?D1,q,v(?0)?D1,q?D2,r?H1,u0?D0,?1,H0?H0,?1 and compatibility conditions.