Smooth global solutions for the two-dimensional euler poisson system

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 (1998) 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. © de Gruyter 2014.