A mean field approach to the quasineutral limit for the Vlasov-Poisson equation

TL;DR

This paper develops a mean field framework to rigorously derive the Kinetic Isothermal Euler system from a regularized N-particle Coulomb system, addressing the combined mean field and quasineutral limits.

Contribution

It introduces a novel approach to handle the combined mean field and quasineutral limits for Coulomb-interacting particles, leading to the derivation of the Kinetic Isothermal Euler system.

Findings

Successfully derives the Kinetic Isothermal Euler system from particle dynamics.

Provides a rigorous mathematical framework for the combined limits.

Extends previous results to higher dimensions (d ≥ 1).

Abstract

This paper concerns the derivation of the Kinetic Isothermal Euler system in dimension $d \geq 1$ from an N-particle system of extended charges with Coulomb interaction. This requires a combined mean field and quasineutral limit for a regularized N-particle system.