The Cauchy problem for the two dimensional Euler-Poisson system

Details The Cauchy problem for the two dimensional Euler-Poisson system The Cauchy problem for the two dimensional Euler-Poisson system

2011-09-27

arxiv.org/abs/1109.5980v4

Physics

Mathematical Physics

29 pages

Scientific paper

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.

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