  This paper is concerned with uniform regularity estimates for a family of
Stokes systems with rapidly oscillating periodic coefficients. We establish
interior Lipschitz estimates for the velocity and $L^\infty$ estimates for the
pressure as well as a Liouville property for solutions in $\mathbb{R}^d$. We
also obtain the boundary $W^{1,p}$ estimates in a bounded $C^1$ domain for any
$1<p<\infty$.
