Uniform global convergence of non-isentropic Euler–Maxwell systems with dissipation

Abstract

The purpose of this paper is to investigate uniformly global smooth solutions to the Cauchy problem for a non-isentropic Euler–Maxwell system with velocity dissipation and small physical parameters. As the parameters go to zero, we prove that the quasi-neutral limit of the non-isentropic Euler–Maxwell system is the e-MHD system and the linear transport equation for temperature, while its non-relativistic quasi-neutral limit is the incompressible Euler equation and the linear transport equation for temperature. The uniform energy estimates are achieved through controlling the divergence and the curl of the velocity, the electric and magnetic fields.