Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions

Marc Briant (1) , Yan Guo (1)

1 Brown University

In a general C 1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (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 (m). Of important note is the fact that the methods do not involve contradiction arguments.

Mots clés: Boltzmann equation; Perturbative theory; Maxwell boundary condi- tions; Specular reflection boundary conditions; Maxwellian diffusion boundary con- ditions Contents

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Marc Briant, Yan Guo. Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions. Journal of Differential Equations, 2016, 261 (12), pp.7000 - 7079. ⟨10.1016/j.jde.2016.09.014⟩. ⟨hal-01492052⟩