Convergence of the Navier-Stokes-Maxwell system to the Euler-Maxwell system near constant equilibrium

The aim of this paper is to provide a justification of the vanishing viscosity limit of the compressible Navier-Stokes-Maxwell system in the whole space. With suitable initial data, we rigorously prove that there exists a sequence of unique smooth solutions of the Navier-Stokes-Maxwell system which converges to the given smooth solution of the Euler-Maxwell system near constant equilibrium when the viscosity coefficients tend to zero. Moreover, a uniform convergence rate is obtained in terms of the viscosity coefficients. As a byproduct, a similar result for the compressible Navier-Stokes-Poisson system is also obtained.