The movement of a solid in an incompressible perfect fluid as a geodesic flow
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
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1102.1380v1
Journal nameProceedings of the American Mathematical Society
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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 / Keywordsleast action principle; Perfect incompressible fluid; fluid-rigid body interaction
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On the motion of a small light body immersed in a two dimensional incompressible perfect fluid with vorticity Glass, Olivier; Lacave, Christophe; Sueur, Franck (2016) Article accepté pour publication ou publié