Instability in a Vlasov-Fokker-Planck binary mixture

TL;DR

This paper investigates the stability of a two-species particle system modeled by Vlasov-Fokker-Planck equations, showing that at low temperatures, the homogeneous equilibrium becomes dynamically unstable under specific perturbations.

Contribution

It demonstrates the instability of homogeneous equilibrium in a Vlasov-Fokker-Planck binary mixture at low temperatures, extending understanding of kinetic model behaviors.

Findings

Homogeneous equilibrium is unstable at low temperature

Instability occurs under certain perturbations

Results extend previous theoretical understanding

Abstract

This paper is concerned with a kinetic model of a Vlasov-Fokker-Planck system used to describe the evolution of two species of particles interacting through a potential and a thermal reservoir at given temperature. We prove that at low temperature, the homogeneous equilibrium is dynamically unstable under certain perturbations. Our work is motivated by a problem arising in \cite{EGM1}.