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 $L^\infty_{ x,v}(m)$. Of important note is the fact that the methods do not involve contradiction arguments.
Categories: math.AP math-ph math.MP