Time evolution of a Vlasov-Poisson plasma with different species and infinite mass in $\mathbb{R}^3$

TL;DR

This paper proves the existence and uniqueness of solutions for a multi-species Vlasov-Poisson plasma in three-dimensional space, accommodating unbounded mass and Coulomb interactions.

Contribution

It extends previous results by establishing well-posedness for systems with infinite mass and mixed charge species in  dimensions.

Findings

Proved existence of solutions with unbounded initial mass.

Established uniqueness of solutions under specified conditions.

Extended prior finite-mass results to infinite-mass plasma models.

Abstract

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both positive or negative charge. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell-Boltzmann law, extending a result obtained by the same authors, which was restricted to finite total mass.