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

Glass, Olivier; Sueur, Franck

Glass, Olivier; Sueur, Franck (2012), The movement of a solid in an incompressible perfect fluid as a geodesic flow, Proceedings of the American Mathematical Society, 140, p. 2155-2168. http://dx.doi.org/10.1090/S0002-9939-2011-11219-X

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1102.1380v1

Date

2012

Journal name

Proceedings of the American Mathematical Society

Volume

140

Publisher

American Mathematical Society

Pages

2155-2168

Abstract (EN)

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.

Subjects / Keywords

least action principle; Perfect incompressible fluid; fluid-rigid body interaction