English

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}
}