Stability of Non-constant Equilibrium Solutions for the Full Compressible Navier–Stokes–Maxwell System

In this article we consider a Cauchy problem for the full compressible Navier–Stokes–Maxwell system arising from viscosity plasmas. This system is quasilinear hyperbolic–parabolic. With the help of techniques of symmetrizers and the smallness of non-constant equilibrium solutions, we establish that global smooth solutions exist and converge to the equilibrium solution as the time approaches infinity. This result is obtained for initial data close to the steady-states. As a byproduct, we obtain the global stability of solutions near the equilibrium states for the full compressible Navier–Stokes–Poisson system in a three-dimensional torus.