Zero dielectric constant limit of the full Magnet-Hydro-Dynamics system

In this paper, we study the zero dielectric constant limit to the full Magnet-Hydro-Dynamics system (or more precisely the Maxwell–Navier–Stokes system). For well prepared initial data, the convergences of solutions of the full MHD system towards to the solutions of the classical 2D parabolic MHD system are justified rigorously by adapting the elaborate energy method as the dielectric constant tends to zero. Furthermore, the corresponding convergence rates are also obtained.