| In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L infinity estimates for the pressure as well as Liouville property for solutions in Rd. We are able to obtain the boundary W1,p estimates in a bounded C 1 domain for any 1 < p < infinity. We also study the convergence rates in L2 and H 1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients. |
