The Cauchy problem for the two dimensional Euler-Poisson system

TL;DR

This paper solves the initial value problem for the two-dimensional Euler-Poisson system, establishing the existence of smooth solutions and confirming conjectures about their behavior similar to the three-dimensional case.

Contribution

It fully resolves the 2D Cauchy problem for the Euler-Poisson system by constructing wave operators and proving the existence of smooth solutions.

Findings

Existence of smooth solutions for the 2D Euler-Poisson system.

Construction of wave operators for the 2D system.

Complete resolution of the 2D Cauchy problem.

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.