Besov regularity for the stationary Navier–Stokes equation on bounded Lipschitz domains

Abstract

We use the scale , , , to study the regularity of the stationary Stokes equation on bounded Lipschitz domains , , with connected boundary. The regularity in these Besov spaces determines the order of convergence of nonlinear approximation schemes. Our proofs rely on a combination of weighted Sobolev estimates and wavelet characterizations of Besov spaces. Using Banach’s fixed point theorem, we extend this analysis to the stationary Navier–Stokes equation with suitable Reynolds number and data, respectively.