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 R 3 which are the coupling between the NavierStokes-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.

Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations

“…For the full multi-dimensional compressible magnetohydrodynamic equations, the existence of variational solutions was established in [4,9,13], while a unique local strong solution was obtained in [10]. The low Mach number limit is a very interesting topic in magnetohydrodynamics, see [20,27,29,31] in the framework of the so-called variational solutions, and [15][16][17] in the framework of the local smooth solutions with small density and temperature variations, or large density/entropy and temperature variations.…”

Entropy-bounded solutions to the 3D compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity

“…We refer to [32,34] for more results on global solutions to multi-dimensional full compressible nonresistive MHD equations. There are some interesting results on other studies of (1.1), such as blow-up criterion of solutions [16,45,49], asymptotic limits of solutions [19][20][21]23], and so on.…”