On the attractive plasma-charge system in 2-d

TL;DR

This paper investigates the dynamics of a 2D plasma with negative point charges, proving the existence of global solutions despite potential density singularities near charges.

Contribution

It establishes the existence of global solutions for the attractive plasma-charge system in two dimensions, addressing challenges posed by unbounded plasma densities.

Findings

Global existence of solutions proven

Handling of unbounded plasma density near charges

Uniqueness remains an open problem

Abstract

We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a global in time solution, assuming a suitable initial distribution of the velocities of the plasma particles. Uniqueness remains unsolved.