Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters

This work is concerned with the two-fluidEuler-Maxwell equations for plasmas with small parameters. We study,by means of asymptotic expansions, the zero-relaxation limit, thenon-relativistic limit and the combined non-relativistic and quasi-neutrallimit. For each limit with well-prepared initial data, we show theexistence and uniqueness of an asymptotic expansion up to any order. Forgeneral data, an asymptotic expansion up to order 1 of thenon-relativistic limit is constructed by taking into account the initiallayers. Finally, we discuss the justification of the limits.