Global strong solutions in $\mathbb{R}^3$ for ionic Vlasov-Poisson systems

TL;DR

This paper proves the existence of global strong solutions for ion Vlasov-Poisson systems in three-dimensional space, advancing the mathematical understanding of plasma models with minimal initial assumptions.

Contribution

It establishes the first global well-posedness results for ion Vlasov-Poisson systems in ^3 with minimal initial data and confining potential assumptions.

Findings

Proved global existence of strong solutions in ^3

Extended well-posedness theory to ion plasma models

Minimal assumptions on initial data and potential

Abstract

Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space $\mathbb{R}^3$, under minimal assumptions on the initial data and the confining potential.