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Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems

Grégoire Loeper
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Abstract

This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart, the Euler-Monge-Ampère system, where the fully non-linear 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.

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Grégoire Loeper. 2005-04-07. Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. https://arxiv.org/abs/math/0504134

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