  We study the stationary Boltzmann equation in a thin slab for a rarefied gas
for which the molecular mean free path is comparable to the film thickness. We
prove that there exists a solution which converges, in the hydrodynamic limit,
to a density Maxwellian -- this density is obtained as the solution to the
generalized Reynolds equation. The convergence is proved using a truncated
Hilbert expansion by carefully estimating the remainder.
