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Remarks on the vanishing obstacle limit for a 3D viscous incompressible fluid
Author(s):
Dragos
Iftimie;
James
P.
Kelliher
Journal:
Proc. Amer. Math. Soc.
137
(2009),
685-694.
MSC (2000):
Primary 76D05
Posted:
September 16, 2008
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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:
-
- 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
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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:
10.1090/S0002-9939-08-09670-6
PII:
S 0002-9939(08)09670-6
Keywords:
Navier-Stokes equations
Received by editor(s):
January 18, 2008
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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