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arXiv · 1608.00821

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

Frank Eckhardt·Petru A. Cioica-Licht·Stephan Dahlke
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Abstract

We use the scale $B^s_{\tau}(L_\tau(\Omega))$, $1/\tau=s/d+1/2$, $s>0$, to study the regularity of the stationary Stokes equation on bounded Lipschitz domains $\Omega\subset\mathbb{R}^d$, $d\geq 3$, 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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Frank Eckhardt, Petru A. Cioica-Licht, Stephan Dahlke. 2016-08-02. Besov Regularity for the Stationary Navier-Stokes Equation on Bounded Lipschitz Domains. https://arxiv.org/abs/1608.00821

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