Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Amp\`ere systems
Analysis of PDEs
2016-09-07 v1 Mathematical Physics
math.MP
Abstract
This paper studies the pressureless Euler-Poisson system and its fully non-linear counterpart, the Euler-Monge-Amp\`ere system, where the fully non-linear Monge-Amp\`ere 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.
Keywords
Cite
@article{arxiv.math/0504134,
title = {Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Amp\`ere systems},
author = {Grégoire Loeper},
journal= {arXiv preprint arXiv:math/0504134},
year = {2016}
}