Asymptotic Stability of the Boltzmann Equation with Maxwell Boundary Conditions

Abstract

In a general $C^1$ domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient $\alpha$ in $(\sqrt{2/3},1]$, and discuss this threshold. We consider polynomial or stretched exponential weights $m(v)$ and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in $L_{x,v}^{\infty }(m)$. Of important note is the fact that the methods do not involve contradiction arguments.

68 pages

References in corpus (4)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• The Boltzmann equation with specular boundary condition in convex domains
• The Boltzmann equation for a multi-species mixture close to global equilibrium
• Stability of global equilibrium for the multi-species Boltzmann equation in $L^{\infty }$ settings

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