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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simple proof of $ L^{q}$-estimates for the steady-state Oseen and Stokes equations in a rotating frame. Part II: Weak solutions


Authors: Giovanni P. Galdi and Mads Kyed
Journal: Proc. Amer. Math. Soc. 141 (2013), 1313-1322
MSC (2010): Primary 35Q30, 35B45, 76D07
Published electronically: August 23, 2012
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Abstract: This is the second of two papers in which simple proofs of $ L^{q}$-estimates of solutions to the steady-state three-dimensional Oseen and Stokes equations in a rotating frame of reference are given. In this part, estimates are established in terms of data in homogeneous Sobolev spaces of negative order.


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Additional Information

Giovanni P. Galdi
Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Email: galdi@pitt.edu

Mads Kyed
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany
Email: kyed@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11640-5
PII: S 0002-9939(2012)11640-5
Received by editor(s): August 9, 2011
Published electronically: August 23, 2012
Additional Notes: The first author was partially supported by NSF grant DMS-1062381
The second author was supported by the DFG and JSPS as a member of the International Research Training Group Darmstadt-Tokyo IRTG 1529.
Communicated by: Walter Craig
Article copyright: © Copyright 2012 American Mathematical Society