The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation
Analysis of PDEs
2012-05-24 v1
Abstract
We consider in this paper the rigorous justification of the Zakharov-Kuznetsov equation from the Euler-Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave small-amplitude limit is described by the Zakharov-Kuznetsov equation. This is done first in the case of cold plasma; we then show how to extend this result in presence of the isothermal pressure term with uniform estimates when this latter goes to zero.
Keywords
Cite
@article{arxiv.1205.5080,
title = {The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation},
author = {David Lannes and Felipe Linares and Jean-Claude Saut},
journal= {arXiv preprint arXiv:1205.5080},
year = {2012}
}