Besov Regularity for the Stationary Navier-Stokes Equation on Bounded Lipschitz Domains

Abstract

We use the scale $B_{\tau }^s(L_{\tau }(\Omega ))$, $1/\tau =s/d+1/2$, $s>0$, to study the regularity of the stationary Stokes equation on bounded Lipschitz domains $\Omega \subset {\mathbb{R}}^d$, $d\ge 3$, 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. By using Banach's fixed point theorem, we extend this analysis to the stationary Navier-Stokes equation with suitable Reynolds number and data, respectively.

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