Besov regularity for the stationary Navier–Stokes equation on bounded Lipschitz domains. Issue 3 (17th February 2018)

• Record Type: Journal Article
• Authors: Eckhardt, Frank; Cioica-Licht, Petru A.; Dahlke, Stephan
• Is Part Of: Applicable analysis. Volume 97:Issue 3(2018)
• Page Start: 466
• Page End: 485
• Publication Date: 2018-02-17
• Subjects: Stokes equation -- Navier–Stokes equation -- Besov space -- weighted Sobolev estimate -- wavelet -- nonlinear approximation -- fixed point theorem; Primary: 35B65 -- 35Q30 -- 76D05 -- 76D07 -- Secondary: 42C40 -- 46E35 -- 65T60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1272103
• Languages: English
• ISSNs: 0003-6811

Abstract

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.