Vanishing resistive limit for the 2D magnetohydrodynamic system with density depend viscosity

This paper is concerned with the compressible isentropic magnetohydrodynamic (MHD) system in a bounded domain of R2 with initial vacuum. We prove the existence and uniqueness of strong solution to the system with density depend viscosity, with a strictly positive resistivity coefficient, in a finite time interval. We also construct the existence and uniqueness of strong solution to the system, when the resistivity coefficient is null. Finally, we establish the convergence rates to the system when the resistivity coefficient tends to zero.