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Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. (English) Zbl 1369.35088
Summary: This work is concerned with the two-fluid Euler-Maxwell equations for plasmas with small parameters. We study, by means of asymptotic expansions, the zero-relaxation limit, the non-relativistic limit and the combined non-relativistic and quasi-neutral limit. For each limit with well-prepared initial data, we show the existence and uniqueness of an asymptotic expansion up to any order. For general data, an asymptotic expansion up to order 1 of the non-relativistic limit is constructed by taking into account the initial layers. Finally, we discuss the justification of the limits.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
35C20 Asymptotic expansions of solutions to PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanical studies of plasmas
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