Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings

TL;DR

This paper proves the stability of global equilibrium for multi-species Boltzmann equations with different masses on a 3D torus, extending recent results to more general kernels and establishing explicit stability thresholds in weighted $L^ abla_{x,v}$ spaces.

Contribution

It extends stability results from mono-species to multi-species Boltzmann equations with different masses and general kernels, providing explicit thresholds in weighted $L^ abla_{x,v}$ spaces.

Findings

Established stability estimates in weighted $L^ abla_{x,v}$ spaces.

Extended recent mono-species estimates to multi-species case.

Provided explicit thresholds for stability in polynomial and exponential weights.

Abstract

We prove the stability of global equilibrium in a multi-species mixture, where the different species can have different masses, on the $3$-dimensional torus. We establish stability estimates in $L^\infty_{x,v}(w)$ where $w=w(v)$ is either polynomial or exponential, with explicit threshold. Along the way we extend recent estimates and stability results for the mono-species Boltzmann operator not only to the multi-species case but also to more general hard potential and Maxwellian kernels.