  The existence and stability of collisional kinetic equation, especially
non-cutoff Boltzmann equation, in bounded domain with physical boundary
condition is longstanding open problem. This work proves the global stability
of the Landau equation and non-cutoff Boltzmann equation in union of cubes with
the specular reflection boundary condition when an initial datum is near
Maxwellian. Moreover, the solution enjoys exponential large-time decay in
bounded domain. Our method is based on that fact that normal derivatives in
cubes is also derivatives along axis, which allows us to obtain high-order
derivative estimates.

Analysis of PDEs