The Boltzmann equation with specular boundary condition in convex   domains
  We establish the global-wellposedness 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 long standing open problem after an announcement of [20] in 1977. 
Chanwoo Kim, Donghyun Lee
math.AP