Incompressible Limit of the Non-isentropic Magnetohydrodynamic Equations in the Half Plane

To study the incompressible limit of the non-isentropic magnetohydrodynamic(MHD)equations with the Dirichlet condition for velocity and perfectly conducting boundary condition for magnetic field in the half plane,the energy method and the general regularity theory are implied,and the existence of solution follows from the Schauder fixed-point theorem and the uniqueness from the Gronwall inequality. Then the uniform estimates in the Mach number,which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary,are estimated within a short time interval independent of Mach number ε ∈(0,1 ,provided that the initial data are well-prepared.Finally,the global existence and uniqueness of solution for MHD equations are obtained.