Initial layers and zero-relaxation limits of Euler–Maxwell equations

In this paper we consider zero-relaxation limits for periodic smooth solutions of Euler–Maxwell systems. For well-prepared initial data, we propose an approximate solution based on a new asymptotic expansion up to any order. For ill-prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates.