  Boundary effects play an important role in the study of hydrodynamic limits
in the Boltzmann theory. We justify rigorously the validity of the hydrodynamic
limit from the Boltzmann equation of soft potentials to the compressible Euler
equations by the Hilbert expansion with multi-scales. Specifically, the
Boltzmann solutions are expanded into three parts: interior part, viscous
boundary layer and Knudsen boundary layer. Due to the weak effect of collision
frequency of soft potentials, new difficulty arises when tackling the existence
of Knudsen layer solutions with space decay rate, which has been overcome under
some constraint conditions and losing velocity weight arguments.
