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Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. (English) Zbl 1077.76072

Summary: This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
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