  This work concerns with boundary conditions (BCs) of the linearized moment
system for rarefied gases. As the Knudsen number is sufficiently small, we
analyze the boundary-layer behaviors of the moment system by resorting to a
three-scale asymptotic expansion. The asymptotic analysis casts the flows into
the outer solution, the viscous layer and the Knudsen layer. Starting from the
BCs of the moment system, we propose a matching requirement and construct BCs
for the Navier-Stokes equations. The obtained BCs contain the effect of
second-order terms on the velocity slip and temperature jump. For the
illustrative case of the Couette flow, we prove the validity of the constructed
BCs through the error estimates. Meanwhile, numerical tests are presented to
show the performance of the constructed BCs.
