Publisher DOI: 10.1016/j.jde.2022.09.001
arXiv ID: 2204.05867v1
Title: The Stokes operator in two-dimensional bounded Lipschitz domains
Language: English
Authors: Gabel, Fabian Nuraddin Alexander  
Tolksdorf, Patrick 
Keywords: Analysis of PDEs; Functional Analysis; Primary 47D06, 35Q30, Secondary 76D03, 76D05, 76D07
Issue Date: 15-Dec-2022
Source: Journal of Differential Equations 340: 227-272 (2022-12-15)
Abstract (english): 
We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain Ω subject to homogeneous Dirichlet boundary conditions. We prove Lᵖ-resolvent estimates for p satisfying 1 / p - 1 / 2 < 1 / 4 + ε for some ε > 0. We further show that the Stokes operator admits the property of maximal regularity and that its H∞-calculus is bounded. This is then used to characterize domains of fractional powers of the Stokes operator. Finally, we give an application to the regularity theory of weak solutions to the Navier-Stokes equations in bounded planar Lipschitz domains.
ISSN: 0022-0396
Journal: Journal of differential equations 
Institute: Mathematik E-10 
Document Type: Article
Peer Reviewed: No
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