  In this paper, we prove the compressible Euler limit from Boltzmann equation
with complete diffusive boundary condition in half-space by employing the
Hilbert expansion which includes interior and Knudsen layers. This rigorously
justifies the corresponding formal analysis in Sone's book
\cite{Sone-2007-Book} in the context of short time smooth solutions. In
particular, different with previous works in this direction, no Prandtl layers
are needed.
