Homogenization of Stokes Systems with Periodic Coefficients
Shu Gu · UKnowledge (University of Kentucky) · 2016
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∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.