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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A steady-state exterior Navier-Stokes problem that is not well-posed


Author: Giovanni P. Galdi
Journal: Proc. Amer. Math. Soc. 137 (2009), 679-684
MSC (2000): Primary 76D05, 76D03; Secondary 76D07
Published electronically: August 15, 2008
MathSciNet review: 2448590
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Abstract: We prove that the exterior Navier-Stokes problem with zero velocity at infinity is not well-posed in homogeneous Sobolev spaces. This result complements and clarifies well-known previous results obtained by various authors.


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Additional Information

Giovanni P. Galdi
Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Email: galdi@engr.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09658-5
PII: S 0002-9939(08)09658-5
Keywords: Navier-Stokes equations, exterior problem, homogeneous Sobolev spaces.
Received by editor(s): January 9, 2008
Published electronically: August 15, 2008
Additional Notes: This work was supported in part by NSF Grant #DMS-0707281.
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.