The Inhomogeneous Dirichlet Problem for the Stokes System in Lipschitz Domains with Unit Normal Close to VMO

The goal of this work is to study the inhomogeneous Dirichlet problem for the Stokes system in a Lipschitz domain $\Omega\subseteq\mathbb{R}^n$, $n\ge 2$. Our main result is that this problem is well posed in Besov–Triebel–Lizorkin spaces, provided that the unit normal $\nu$ to $\Omega$ has small mean oscillation.