4 citations · 4 across the 5 of their papers we have counts for
6 papers
-calculus for Stokes operators on rough and on unbounded domains
Peer Christian Kunstmann, Patrick Tolksdorf
In this article, we give an overview on known as well as new results on the boundedness of the -calculus of the Stokes operator in rough as well as in unbounded (smooth…
Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains
Matthias Hieber, Hideo Kozono, Sylvie Monniaux +1
Consider the coupled Keller-Segel-Navier-Stokes or the chemotaxis-consumption-Navier-Stokes system in bounded Lipschitz domains for general coupling terms which, e.g., include buoy…
On Kato's Square Root Property for the Generalized Stokes Operator
Luca Haardt, Patrick Tolksdorf
We establish the Kato square root property for the generalized Stokes operator on with bounded measurable coefficients. More precisely, we identify the domain of the…
Free Boundary Problems via Da Prato-Grisvard Theory
Raphaël Danchin, Matthias Hieber, Piotr B. Mucha +1
An -maximal regularity theory for parabolic evolution equations inspired by the pioneering work of Da Prato and Grisvard is developed. Besides of its own interest, th…
-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients
Patrick Tolksdorf
The aim of this article is to deepen the understanding of the derivation of -estimates of non-local operators. We review the -extrapolation theorem of S…
On the -theory of the Navier--Stokes equations on three-dimensional bounded Lipschitz domains
Patrick Tolksdorf
On a bounded Lipschitz domain , , we continue the study of Shen and of Kunstmann and Weis of the Stokes operator on . We employ…