Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Remarks on the vanishing obstacle limit for a 3D viscous incompressible fluid


Authors: Dragos Iftimie and James P. Kelliher
Journal: Proc. Amer. Math. Soc. 137 (2009), 685-694
MSC (2000): Primary 76D05
DOI: https://doi.org/10.1090/S0002-9939-08-09670-6
Published electronically: September 16, 2008
MathSciNet review: 2448591
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In [Math. Ann. 336 (2006), 449-489], the authors consider the two-dimensional Navier-Stokes equations in the exterior of an obstacle shrinking to a point and determine the limit velocity. Here we consider the same problem in the three-dimensional case, proving that the limit velocity is a solution of the Navier-Stokes equations in the full space.


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

  • 1. G. P. Galdi,
    An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, volume 38 of Springer Tracts in Natural Philosophy.
    Springer-Verlag, New York, 1994.
  • 2. E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951), 213-231. MR 0050423 (14:327b)
  • 3. D. Iftimie, M. C. Lopes Filho, and H. J. Nussenzveig Lopes, Two dimensional incompressible ideal flow around a small obstacle, Comm. Part. Diff. Eqns. 28 (2003), no. 1-2, 349-379. MR 1974460 (2004d:76009)
  • 4. -, Two-dimensional incompressible viscous flow around a small obstacle, Math. Ann. 336 (2006), no. 2, 449-489. MR 2244381 (2007d:76050)
  • 5. M. C. Lopes Filho, Vortex dynamics in a two-dimensional domain with holes and the small obstacle limit, SIAM J. Math. Anal. 39 (2007), no. 2, 422-436. MR 2338413

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 76D05

Retrieve articles in all journals with MSC (2000): 76D05


Additional Information

Dragos Iftimie
Affiliation: Université de Lyon, Université Lyon 1, CNRS, UMR 5208 Institut Camille Jordan, Bâtiment du Doyen Jean Braconnier, 43, Blvd. du 11 Novembre 1918, F–69622 Villeurbanne Cedex, France
Email: dragos.iftimie@univ-lyon1.fr

James P. Kelliher
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, California 92521
Email: kelliher@math.ucr.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09670-6
Keywords: Navier-Stokes equations
Received by editor(s): January 18, 2008
Published electronically: September 16, 2008
Additional Notes: The second author was supported in part by NSF grant DMS-0705586 during the period of this work
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society