  We consider the nonlinear boundary layers of the Boltzmann equation in a
three-dimensional half-space by perturbing around a Maxwellian, under the
assumption that the Mach number of the Maxwellian satisfies ${\cal M}_{\infty}
< -1$. In preceding works, nonlinear boundary layers of the Boltzmann equation
in a half-line are considered, with stationary solutions obtained and nonlinear
stability confirmed. In this paper, we establish the unique existence of
stationary solutions for the three-dimensional half-space model, and show that
the stationary solution is asymptotic stable.
