Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions

作者：Briant Marc; Guo Yan

来源：Journal of Differential Equations, 2016, 261(12): 7000-7079.

DOI：10.1016/j.jde.2016.09.014

• Boltzmann equation
• Perturbative theory
• Maxwell boundary conditions
• Specular reflection boundary conditions
• Maxwellian diffusion boundary conditions

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 (root 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(infinity), (m). Of important note is the fact that the methods do not involve contradiction arguments.

• 出版日期2016-12-15