Neumann problems for the Stokes equations in convex domains

Abstract

This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $R^d$. We obtain nontangential maximal function estimates in $L^p$ and $W^{1,p}$ estimates for p in certain ranges depending on d. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a $W^{2,2}$ estimate for the Stokes equations in convex domains.