The 2D Euler-Poisson System with Spherical Symmetry

TL;DR

This paper proves the global existence of smooth, small-amplitude solutions to the 2D Euler-Poisson system under spherical symmetry, overcoming challenges posed by slow decay rates in the linearized system.

Contribution

It demonstrates the existence of global smooth solutions for the 2D Euler-Poisson system with spherical symmetry, extending previous work to handle slow decay issues.

Findings

Global-in-time smooth solutions exist for small initial data

Radial symmetry is crucial for controlling slow decay

Addresses challenges of slow decay in 2D Euler-Poisson system

Abstract

This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa, Tsutaya, and Tsutsumi's work, we show that such smooth solutions exist for radially symmetric flows.