Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. 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)
  • 2. 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
  • 3. 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
  • 4. 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)
  • 5. -, Steady flow of a Navier-Stokes fluid around a rotating obstacle, Journal of Elasticity 71 (2003), 1-31. MR 2042672 (2005c:76030)
  • 6. 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
  • 7. 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)
  • 8. 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.
  • 9. Carl Wilhelm Oseen, Hydrodynamik, Akademische Verlagsgesellschaft M.B.H., Leipzig, 1927.

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 35Q30, 76D05, 35B40, 35C20

Retrieve articles in all journals with MSC (2010): 35Q30, 76D05, 35B40, 35C20

Additional Information

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

DOI: https://doi.org/10.1090/S0033-569X-2013-01288-7
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.

American Mathematical Society