The zero-energy limit and quasi-neutral limit of scaled Euler-Maxwell system and its corresponding limiting models

In this paper, we apply a new scaling for Euler-Maxwell system. As a result, zero-energy limit is introduced, combining it with quasi-neutral limit, we obtain a complete system of the limiting models for Euler-Maxwell system. The asymptotic analysis and a weighted energy method arc used to rigorously justify the zero-energy limit for e-MHD, which is the limiting model of Euler-Maxwell system as the Debye length tends to zero. For other limits, we provide a formal derivation and obtain an approximate asymptotic expansion.