Convergence of the Full Compressible Navier–Stokes–Maxwell System to the Incompressible Magnetohydrodynamic Equations in a Bounded Domain II: Global Existence Case

Abstract

In this paper we continue our study on the establishment of uniform estimates of strong solutions with respect to the Mach number and the dielectric constant to the full compressible Navier–Stokes–Maxwell system in a bounded domain \(\Omega \subset \mathbb {R}^3\). In Fan et al. (Kinet Relat Models 9:443–453, 2016), the uniform estimates have been obtained for large initial data in a short time interval. Here we shall show that the uniform estimates exist globally if the initial data are small. Based on these uniform estimates, we obtain the convergence of the full compressible Navier–Stokes–Maxwell system to the incompressible magnetohydrodynamic equations for well-prepared initial data.