Smooth global solutions for the two dimensional Euler Poisson system

2011/09/18 by Jang, Juhi, Li, Dong, Zhang, Xiaoyi
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1109.3882

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 \citeGuo98 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.

Related

• The Cauchy problem for the two dimensional Euler-Poisson system
• The Euler--Poisson system in 2D: global stability of the constant\n equilibrium solution
• The Global Well-posedness of the Euler-Poisson System for Ions in 2D
• Non-neutral global solutions for the electron Euler-Poisson system in 3D
• Global solutions for the two dimensional Euler-Poisson system with\n attractive forcing