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

Marc  Briant

doi:10.3934/dcds.2016090

Article Contents

2016, Volume 36, Issue 12: 6669-6688. Doi: 10.3934/dcds.2016090

This issue Previous Article Linear response in the intermittent family: Differentiation in a weighted $C^0$-norm Next Article Calderón-Zygmund estimate for homogenization of parabolic systems

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

Marc Briant^1,

1.
Sorbonne Universités, UPMC Univ. Paris 06/ CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris

Received: February 29, 2016

Revised: June 30, 2016

Published: May 2017

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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.

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Mathematics Subject Classification: Primary: 35B40, 35Q20; Secondary: 76P05, 82C40.

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References

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