The Global Well-posedness of the Euler-Poisson System for Ions in 2D

TL;DR

This paper proves the global well-posedness of the 2D Euler-Poisson system for ions, addressing challenges from low-frequency resonances and slow decay by adapting advanced analytical methods.

Contribution

It introduces a novel approach by applying techniques from gravity-capillary water waves and Euler-Maxwell systems to the Euler-Poisson system in 2D.

Findings

Established global well-posedness for the system

Overcame low-frequency resonance challenges

Extended methods from water waves and Euler-Maxwell systems

Abstract

This paper aims to establish the global well-posedness of the Euler-Poisson system for ions in 2D. The difficulties arising from time resonance at low frequencies and slow decay will be overcome by applying the method developed for the gravity-capillary water waves and Euler-Maxwell systems.