Uniform well-posedness and singular limits of the isentropic Navier–Stokes–Maxwell system in a bounded domain

Abstract

We prove the global-in-time and uniform-in-${(\epsilon_1,\epsilon_2)}$ of strong solutions to the isentropic Navier–Stokes–Maxwell system in a bounded domain, when ${\epsilon_1}$ is the Mach number, and ${\epsilon_2}$ is the dielectric constant. Consequently, we obtain the convergences of compressible Navier–Stokes–Maxwell system to the incompressible Navier–Stokes–Maxwell system (${\epsilon_1\rightarrow 0}$ and ${\epsilon_2}$ fixed), the compressible magnetohydrodynamic equations (${\epsilon_1}$ fixed and ${\epsilon_2\rightarrow 0}$) or the incompressible magnetohydrodynamic equations (${\epsilon_1\rightarrow 0}$ and ${\epsilon_2\rightarrow 0}$) for well-prepared data.