  Boundary effects play an important role in the study of hydrodynamic limits
in the Boltzmann theory. Based on a systematic derivation and study of the
viscous layer equations and the $L^2$ to $L^\infty$ framework, we establish the
validity of the Hilbert expansion for the Boltzmann equation with specular
reflection boundary conditions, which leads to derivations of compressible
Euler equations and acoustic equations.
