3D viscous incompressible fluid around one thin obstacle
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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.References
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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
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3314124