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

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 $L_{x,v}^{\infty }(w)$ 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.

22 pages

References in corpus (2)

• Asymptotic Stability of the Boltzmann Equation with Maxwell Boundary Conditions
• The Boltzmann equation for a multi-species mixture close to global equilibrium

Cited by in corpus (4)

• Asymptotic Stability of the Boltzmann Equation with Maxwell Boundary Conditions
• Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions
• Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures
• Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann Equations