The Boltzmann Equation with Specular Boundary Condition in Convex Domains

摘要

>We establish the global well‐posedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the longstanding open problem after an announcement by Shizuta and Asano in 1977. ? 2017 Wiley Periodicals, Inc.