Global Smooth Ion Dynamics in the Euler-Poisson System

TL;DR

This paper develops a mathematical framework to establish the existence of global smooth solutions for ion dynamics in the Euler-Poisson system, complementing previous work on electron behavior, thus advancing plasma modeling.

Contribution

It introduces the first construction of global smooth irrotational solutions with small amplitude for ion dynamics in the Euler-Poisson system.

Findings

Established global smooth solutions for ion dynamics

Extended understanding of plasma behavior in Euler-Poisson models

Complemented prior results on electron dynamics

Abstract

A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were constructed in Guo due to dispersive effect of the electric field. In this paper, we construct global smooth irrotational solutions with small amplitude for ion dynamics in the Euler-Poisson system.