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Proceedings of the American Mathematical Society
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
Published electronically: September 16, 2008
MathSciNet review: 2448591
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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.


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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: http://dx.doi.org/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
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.