A simple proof of estimates for the steadystate 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), 13131322
MSC (2010):
Primary 35Q30, 35B45, 76D07
Published electronically:
August 23, 2012
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Additional Information
Abstract: This is the second of two papers in which simple proofs of estimates of solutions to the steadystate threedimensional 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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 Reinhard Farwig, An analysis of viscous fluid flow past a rotating obstacle, Tohoku Math. J. (2) 58 (2006), no. 1, 129147. MR 2221796 (2007f:35226)
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 , On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, Friedlander, S. et al. (eds.), Handbook of mathematical fluid dynamics. Vol. 1. Amsterdam: Elsevier. 653791, 2002. MR 1942470 (2003j:76024)
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 , Steady flow of a NavierStokes fluid around a rotating obstacle, Journal of Elasticity 71 (2003), 131. MR 2042672 (2005c:76030)
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 Giovanni P. Galdi and Mads Kyed, A simple proof of estimates for the steadystate Oseen and Stokes equations in a rotating frame. Part I: Strong solutions, 2011. To appear in Proc. Amer. Math. Soc.
 [GK11b]
 , Steadystate NavierStokes flows past a rotating body: Leray solutions are physically reasonable, Arch. Ration. Mech. Anal. 200 (2011), no. 1, 2158. MR 2781585 (2012c:35324)
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 Toshiaki Hishida, estimates of weak solutions to the stationary Stokes equations around a rotating body, J. Math. Soc. Japan 58 (2006), no. 3, 743767. MR 2254409 (2007e:35226)
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 Stanislav Kračmar, Šárka Nečasová, and Patrick Penel, approach to weak solutions of the Oseen flow around a rotating body, Rencławowicz, Joanna et al. (eds.), Parabolic and NavierStokes equations. Part 1. Proceedings of the conference, Bedlewo, Poland, September 1017, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 81, Pt. 1, 259276, 2008. MR 2547463 (2010d:35002)
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 Olga A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Second English edition, Gordon and Breach Science Publishers, New York, 1969. MR 0254401 (40:7610)
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 Ana Leonor Silvestre, On the existence of steady flows of a NavierStokes liquid around a moving rigid body, Math. Methods Appl. Sci. 27 (2004), no. 12, 13991409. MR 2069156 (2005f:35251)
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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, D64289 Darmstadt, Germany
Email:
kyed@mathematik.tudarmstadt.de
DOI:
http://dx.doi.org/10.1090/S000299392012116405
PII:
S 00029939(2012)116405
Received by editor(s):
August 9, 2011
Published electronically:
August 23, 2012
Additional Notes:
The first author was partially supported by NSF grant DMS1062381
The second author was supported by the DFG and JSPS as a member of the International Research Training Group DarmstadtTokyo IRTG 1529.
Communicated by:
Walter Craig
Article copyright:
© Copyright 2012
American Mathematical Society
