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3D viscous incompressible fluid around one thin obstacle


Author: C. Lacave
Journal: Proc. Amer. Math. Soc. 143 (2015), 2175-2191
MSC (2010): Primary 35Q30, 76D05, 35Q35
DOI: https://doi.org/10.1090/S0002-9939-2014-12409-9
Published electronically: December 11, 2014
MathSciNet review: 3314124
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Abstract: In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular, we will prove that a solid curve has no effect on the motion of a viscous fluid, so it is a removable singularity for these equations.


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Additional Information

C. Lacave
Affiliation: Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586 - CNRS, Université Paris-Diderot (Paris 7), Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France
Address at time of publication: Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathémathiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06, F-75013, Paris, France
Email: lacave@math.jussieu.fr, christoph.lacave@imj-prg.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-12409-9
Keywords: Navier-Stokes equations, thin obstacles, removable singularity
Received by editor(s): November 12, 2013
Published electronically: December 11, 2014
Additional Notes: The author was partially supported by the Agence Nationale de la Recherche, Project MathOcéan, grant ANR-08-BLAN-0301-01 and by the Project “Instabilities in Hydrodynamics” funded by Paris city hall (program “Emergences”) and the Fondation Sciences Mathématiques de Paris
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society