Smooth global solutions for the two dimensional Euler Poisson system
Analysis of PDEs
2011-09-21 v2 Mathematical Physics
math.MP
Abstract
The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. By using the dispersive Klein-Gordon effect, Guo \cite{Guo98} first constructed a global smooth irrotational solution in the three dimensional case. It has been conjectured that same results should hold in the two-dimensional case. The main difficulty in 2D comes from the slow dispersion of the linear flow and certain nonlocal resonant obstructions in the nonlinearity. In this paper we develop a new method to overcome these difficulties and construct smooth global solutions for the 2D Euler-Poisson system.
Cite
@article{arxiv.1109.3882,
title = {Smooth global solutions for the two dimensional Euler Poisson system},
author = {Juhi Jang and Dong Li and Xiaoyi Zhang},
journal= {arXiv preprint arXiv:1109.3882},
year = {2011}
}
Comments
49 pages