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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.

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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