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The movement of a solid in an incompressible perfect fluid as a geodesic flow

Authors: Olivier Glass and Franck Sueur
Journal: Proc. Amer. Math. Soc. 140 (2012), 2155-2168
MSC (2010): Primary 76B99, 74F10
Published electronically: October 4, 2011
MathSciNet review: 2888201
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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

Franck Sueur
Affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, 4 Place Jussieu, 75005 Paris, France

Keywords: Perfect incompressible fluid, fluid-rigid body interaction, least action principle
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.