Asymptotic profile of a linearized Navier-Stokes flow past a rotating body
Author:
Mads Kyed
Journal:
Quart. Appl. Math. 71 (2013), 489-500
MSC (2010):
Primary 35Q30, 76D05, 35B40, 35C20
DOI:
https://doi.org/10.1090/S0033-569X-2013-01288-7
Published electronically:
May 17, 2013
MathSciNet review:
3112824
Full-text PDF Free Access
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Abstract: Consider a rigid body in a three-dimensional Navier-Stokes liquid moving with a nonzero velocity and rotating with a nonzero angular velocity that are both constant when referred to a frame attached to the body. Linearizing the associated steady-state equations of motion, we obtain the exterior domain Oseen equations in a rotating frame of reference. We analyze the structure of weak solutions to these equations and identify the leading term in the asymptotic expansion of the corresponding velocity field.
References
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- Paul Deuring, Stanislav Kračmar, and Šárka Nečasová, On pointwise decay of linearized stationary incompressible viscous flow around rotating and translating bodies, SIAM J. Math. Anal. 43 (2011), no. 2, 705–738. MR 2784873, DOI https://doi.org/10.1137/100786198
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- Giovanni P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, Springer Tracts in Natural Philosophy, vol. 38, Springer-Verlag, New York, 1994. Linearized steady problems. MR 1284205
- Giovanni P. Galdi, Steady flow of a Navier-Stokes fluid around a rotating obstacle, J. Elasticity 71 (2003), no. 1-3, 1–31. Essays and papers dedicated to the memory of Clifford Ambrose Truesdell III, Vol. II. MR 2042672, DOI https://doi.org/10.1023/B%3AELAS.0000005543.00407.5e
- Giovanni P. Galdi and Mads Kyed, Steady-state Navier-Stokes flows past a rotating body: Leray solutions are physically reasonable, Arch. Ration. Mech. Anal. 200 (2011), no. 1, 21–58. MR 2781585, DOI https://doi.org/10.1007/s00205-010-0350-6
- Giovanni P. Galdi and Ana L. Silvestre, The steady motion of a Navier-Stokes liquid around a rigid body, Arch. Ration. Mech. Anal. 184 (2007), no. 3, 371–400. MR 2299756, DOI https://doi.org/10.1007/s00205-006-0026-4
- Jean Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique, J. Math. Pures Appl. 12 (1933), 1–82.
- Carl Wilhelm Oseen, Hydrodynamik, Akademische Verlagsgesellschaft M.B.H., Leipzig, 1927.
References
- I-Dee Chang and Robert Finn, On the solutions of a class of equations occurring in continuum mechanics, with application to the Stokes paradox, Arch. Rational Mech. Anal. 7 (1961), 388–401. MR 0123803 (23:A1125)
- Paul Deuring, Stanislav Kračmar, and Šárka Nečasová, On pointwise decay of linearized stationary incompressible viscous flow around rotating and translating bodies, SIAM J. Math. Anal. 43 (2011), no. 2, 705–738. MR 2784873
- Reinhard Farwig and Toshiaki Hishida, Asymptotic profile of steady Stokes flow around a rotating obstacle, Technische Universität Darmstadt, FB Mathematik, Preprint 2578, 2009. MR 2844813
- Giovanni P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I: Linearized steady problems, Springer Tracts in Natural Philosophy. 38. New York: Springer-Verlag, 1994. MR 1284205 (95i:35216a)
- ---, Steady flow of a Navier-Stokes fluid around a rotating obstacle, Journal of Elasticity 71 (2003), 1–31. MR 2042672 (2005c:76030)
- Giovanni P. Galdi and Mads Kyed, Steady-State Navier-Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable, Arch. Rational Mech. Anal. 200 (2011), no. 1, 21–58. MR 2781585
- Giovanni P. Galdi and Ana L. Silvestre, The steady motion of a Navier-Stokes liquid around a rigid body, Arch. Rational Mech. Anal. 184 (2007), no. 3, 371–400. MR 2299756 (2008k:35354)
- Jean Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique, J. Math. Pures Appl. 12 (1933), 1–82.
- Carl Wilhelm Oseen, Hydrodynamik, Akademische Verlagsgesellschaft M.B.H., Leipzig, 1927.
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Additional Information
Mads Kyed
Affiliation:
Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany
MR Author ID:
832297
Email:
kyed@mathematik.tu-darmstadt.de
Received by editor(s):
August 15, 2011
Published electronically:
May 17, 2013
Additional Notes:
Supported by the DFG and JSPS as a member of the International Research Training Group Darmstadt-Tokyo IRTG 1529.
Article copyright:
© Copyright 2013
Brown University
The copyright for this article reverts to public domain 28 years after publication.
