Smooth global solutions for the two dimensional Euler Poisson system

TL;DR

This paper proves the existence of smooth, global solutions for the two-dimensional Euler-Poisson system by overcoming dispersive and nonlinear challenges using a novel method.

Contribution

It introduces a new approach to establish global smooth solutions for the 2D Euler-Poisson system, extending previous 3D results to two dimensions.

Findings

Successfully constructed smooth global solutions in 2D

Overcame slow dispersion and nonlocal resonant obstructions

Developed a new analytical method for 2D plasma models

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.