Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus

TL;DR

This paper proves the global existence and uniqueness of solutions with bounded density for the Vlasov-Poisson system with massless electrons in 3D, filling a significant gap in plasma physics mathematical theory.

Contribution

It establishes the first global well-posedness results for the Vlasov-Poisson system with massless electrons in three dimensions, extending previous results for the classical VP system.

Findings

Proved uniqueness of solutions with bounded density.

Established global existence for a broad class of initial data.

Generalized previous results from the classical VP system to VPME.

Abstract

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonlinearity that creates several mathematical difficulties. In particular, while global well-posedness in 3D is well understood in the electron case, this problem remained completely open for the ion model with massless electrons. The aim of this paper is to fill this gap by proving uniqueness for VPME in the class of solutions with bounded density, and global existence of solutions with bounded density for a general class of initial data, generalising all the previous results known for VP.