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The Stokes operator in two-dimensional bounded Lipschitz domains
Publikationstyp
Journal Article
Date Issued
2022-12-15
Sprache
English
Author(s)
Gabel, Fabian Nuraddin Alexander
Institut
Volume
340
Start Page
227
End Page
272
Citation
Journal of Differential Equations 340: 227-272 (2022-12-15)
Publisher DOI
Scopus ID
ArXiv ID
Peer Reviewed
false
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.
Subjects
Analysis of PDEs
Functional Analysis
Primary 47D06, 35Q30, Secondary 76D03, 76D05, 76D07
DDC Class
510: Mathematik