Convergence of the nonisentropic Euler–Maxwell equations to compressible Euler–Poisson equations

Abstract

This paper is concerned with the convergence of the time-dependent and nonisentropic Euler–Maxwell equations to compressible Euler–Poisson equations in a torus via the nonrelativistic limit. By using the method of formal asymptotic expansions, we analyze the nonrelativistic limit for periodic problems with the prepared initial data. It is shown that the small parameter problem has unique solutions existing in the finite time interval where the corresponding limit problems have smooth solutions. Furthermore, the convergence of solutions is rigorously justified.