Access the full text.
Sign up today, get DeepDyve free for 14 days.
W. Desch, Matthias Hieber, J. Prüss (2001)
$ L^p $-Theory of the Stokes equation in a half spaceJournal of Evolution Equations, 1
H. Triebel (1978)
Interpolation Theory, Function Spaces, Differential Operators
J. Francia, F. Ruiz, J. Torrea (1986)
Calderón-Zygmund theory for operator-valued kernelsAdvances in Mathematics, 62
J. Diestel, H. Jarchow, A. Tonge (1995)
Absolutely Summing Operators
R. Farwig (2003)
Weighted $L^q$-Helmholtz decompositions in infinite cylinders and in infinite layersAdvances in Differential Equations
H. Abels (2005)
Reduced and Generalized Stokes Resolvent Equations in Asymptotically Flat Layers, Part II: H∞-CalculusJournal of Mathematical Fluid Mechanics, 7
Andreas Fröhlich (2003)
The Stokes Operator in Weighted $L^{q}$-Spaces I: Weighted Estimates for the Stokes Resolvent Problem in a Half SpaceJournal of Mathematical Fluid Mechanics, 5
R. Denk, Matthias Hieber, F. Bertola, C. Kharif (2003)
Fourier multipliers and problems of elliptic and parabolic type
A. Fröhlich (2007)
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularityMathematische Annalen, 339
J. García-cuerva, J. Francia (1985)
Weighted norm inequalities and related topics
M. Cowling, I. Doust, Alan Micintosh, A. Yagi (1996)
Banach space operators with a bounded H∞ functional calculusJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 60
H. Abels (2005)
Reduced and Generalized Stokes Resolvent Equations in Asymptotically Flat Layers, Part I: Unique SolvabilityJournal of Mathematical Fluid Mechanics, 7
R. Farwig, H. Sohr (1997)
Weighted $L^{q}$-theory for the Stokes resolvent in exterior domainsJournal of The Mathematical Society of Japan, 49
R. Farwig, H. Sohr (1994)
Generalized resolvent estimates for the Stokes system in bounded and unbounded domainsJournal of The Mathematical Society of Japan, 46
G. Galdi (1994)
Linearized steady problems
H. Abels, M. Wiegner (2005)
Resolvent estimates for the Stokes operator on an infinite layerDifferential and Integral Equations
G. Schneider (1998)
Nonlinear Stability of Taylor Vortices in Infinite CylindersArchive for Rational Mechanics and Analysis, 144
R. Farwig, Ri Myong-Hwan (2008)
Resolvent Estimates and Maximal Regularity in Weighted Lq-spaces of the Stokes Operator in an Infinite CylinderJournal of Mathematical Fluid Mechanics, 10
R. Denk, G. Dore, Matthias Hieber, J. Prüss, Alberto Venni (2004)
New thoughts on old results of R.T. SeeleyMathematische Annalen, 328
G. Dore, Alberto Venni (1987)
On the closedness of the sum of two closed operatorsMathematische Zeitschrift, 196
W. Borchers, H. Sohr (1987)
On the semigroup of the Stokes operator for exterior domains inLq-spacesMathematische Zeitschrift, 196
A. Noll, J. Saal (2003)
H∞-calculus for the Stokes operator on Lq-spacesMathematische Zeitschrift, 244
G. Galdi (1994)
An Introduction to the Mathematical Theory of the Navier-Stokes Equations : Volume I: Linearised Steady Problems
Y. Giga (1981)
Analyticity of the semigroup generated by the Stokes operator inLr spacesMathematische Zeitschrift, 178
R. Farwig, H. Sohr (1996)
HELMHOLTZ DECOMPOSITION AND STOKES RESOLVENT SYSTEM FOR APERTURE DOMAINS IN Lq-SPACES, 16
R. Farwig (1996)
Note on the flux condition and pressure drop in the resolvent problem of the Stokes systemmanuscripta mathematica, 89
It is proved that the Stokes operator in L q -space on an infinite cylindrical domain of $${{\mathbb{R}^{n}}}$$ , $${{n \geq 3}}$$ , with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded $${{H^{\infty}}}$$ -calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight cylinder with bounded cross-section $${{\Sigma}}$$ is studied in L q $${{(\mathbb{R}; L^{r}_{\omega} (\Sigma))}}$$ where $${{1 < q,r < \infty}}$$ and $${{\omega \, \epsilon \, A_{r}(\mathbb{R}^{n-1})}}$$ is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on $${{\mathcal{R}}}$$ -boundedness of operator families and on square function estimates involving Muckenhoupt weights.
Journal of Evolution Equations – Springer Journals
Published: Aug 1, 2007
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.