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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The movement of a solid in an incompressible perfect fluid as a geodesic flow
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by Olivier Glass and Franck Sueur PDF
Proc. Amer. Math. Soc. 140 (2012), 2155-2168 Request permission

Abstract:

The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain has recently been studied under its PDE formulation. In particular, classical solutions have been shown to exist locally in time. In this paper, following the celebrated result of Arnold concerning the case of a perfect incompressible fluid alone, we prove that these classical solutions are the geodesics of a Riemannian manifold of infinite dimension, in the sense that they are the critical points of an action, which is the integral over time of the total kinetic energy of the fluid-rigid body system.
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Additional Information
  • Olivier Glass
  • Affiliation: Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
  • Email: glass@ceremade.dauphine.fr
  • Franck Sueur
  • Affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, 4 Place Jussieu, 75005 Paris, France
  • Email: fsueur@ann.jussieu.fr
  • Received by editor(s): February 7, 2011
  • Published electronically: October 4, 2011
  • Additional Notes: The authors were partially supported by the Agence Nationale de la Recherche, Project CISIFS, grant ANR-09-BLAN-0213-02.
  • Communicated by: Walter Craig
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 2155-2168
  • MSC (2010): Primary 76B99, 74F10
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11219-X
  • MathSciNet review: 2888201