Asymptotic Limits of the Full Compressible Magnetohydrodynamic Equations

Abstract

The paper deals with the asymptotic limits of the full compressible magnetohydrodynamic (MHD) equations in the whole space $\mathbb{R}^3$ which are the coupling between the Navier--Stokes--Fourier system with the Maxwell equations governing the behavior of the magnetic field. It is rigorously shown that for the general initial data, the weak solutions of the full compressible MHD equations converge to the strong solution of the ideal incompressible MHD equations as the Mach number, the viscosity coefficients, the heat conductivity, and the magnetic diffusion coefficient go to zero simultaneously. Furthermore, the convergence rates are also obtained.