Transverse asymptotic stability of line solitary waves for the Ionic Euler-Poisson system

TL;DR

This paper proves the stability and describes the long-term behavior of small amplitude solitary waves in a 3D ionic Euler-Poisson system, demonstrating global solutions under small perturbations.

Contribution

It establishes the linear and nonlinear asymptotic stability of line solitary waves in the 3D Euler-Poisson system, a novel result for this model.

Findings

Existence of global smooth solutions for small perturbations.

Asymptotic stability of solitary waves.

Description of long-term behavior of solutions.

Abstract

We prove the linear and nonlinear asymptotic stability of small amplitude one-dimensional solitary waves submitted to small localized irrotational perturbations in the three dimensional Euler-Poisson system describing the dynamics of ions. In particular, in this regime, we obtain the existence of global smooth solutions and describe their asymptotic behavior.