Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions

In a general C1C1 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)m(v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞(m). Of important note is the fact that the methods do not involve contradiction arguments.