The Euler--Poisson system in 2D: global stability of the constant equilibrium solution

TL;DR

This paper proves that small smooth disturbances in a 2D repulsive Euler-Poisson system for electrons persist indefinitely without forming shocks, demonstrating global stability of the constant equilibrium.

Contribution

It extends Guo's 1D results to 2D, establishing global stability for the Euler-Poisson system in two dimensions.

Findings

Small smooth perturbations remain globally smooth in 2D.

The constant equilibrium is globally stable under small perturbations.

No shock formation occurs in the 2D system for small initial disturbances.

Abstract

We consider the (repulsive) Euler-Poisson system for the electrons in two dimensions and prove that small smooth perturbations of a constant background exist for all time and remain smooth (never develop shocks). This extends to 2D the work of Guo.