|arXiv ID:||2204.05867v1||Title:||The Stokes operator in two-dimensional bounded Lipschitz domains||Language:||English||Authors:||Gabel, Fabian Nuraddin Alexander
|Keywords:||Analysis of PDEs;Functional Analysis;Primary 47D06, 35Q30, Secondary 76D03, 76D05, 76D07||Issue Date:||12-Apr-2022||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.
|URI:||http://hdl.handle.net/11420/12669||Institute:||Mathematik E-10||Document Type:||Preprint||Peer Reviewed:||No|
|Appears in Collections:||Publications without fulltext|
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