The Cauchy problem for the two dimensional Euler-Poisson system
Mathematical Physics
2013-11-25 v5 Analysis of PDEs
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. In the 3D case Guo first constructed a global smooth irrotational solution by using dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work, we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system. In this work we completely settle the 2D Cauchy problem.
Keywords
Cite
@article{arxiv.1109.5980,
title = {The Cauchy problem for the two dimensional Euler-Poisson system},
author = {Dong Li and Yifei Wu},
journal= {arXiv preprint arXiv:1109.5980},
year = {2013}
}
Comments
56 pages, to appear in JEMS