  This paper is concerned with the quantitative homogenization of the steady
Stokes equations with the Dirichlet condition in a periodically perforated
domain. Using a compactness method, we establish the large-scale interior
$C^{1, \alpha}$ and Lipschitz estimates for the velocity as well as the
corresponding estimates for the pressure. These estimates, when combined with
the classical regularity estimates for the Stokes equations, yield the uniform
Lipschitz estimates. As a consequence, we also obtain the uniform $W^{k, p}$
estimates for $1<p<\infty$.
