Rigorous derivation of incompressible type Euler equations from non-isentropic Euler–Maxwell equations

In this paper, we investigate the convergence of the time-dependent and non-isentropic Euler–Maxwell equations to incompressible Euler equations in a torus via the combined quasi-neutral and non-relativistic limit. For well prepared initial data, the convergences of solutions of the former to the solutions of the latter are justified rigorously by an analysis of asymptotic expansions and energy method.