The movement of a solid in an incompressible perfect fluid as a geodesic flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2011
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| _version_ | 1866909440440008704 |
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| author | Glass, Olivier Sueur, Franck |
| author_facet | Glass, Olivier Sueur, Franck |
| contents | The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist locally in time. In this note, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1102_1380 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | The movement of a solid in an incompressible perfect fluid as a geodesic flow Glass, Olivier Sueur, Franck Analysis of PDEs 76B99, 74F10 The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist locally in time. In this note, 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. |
| title | The movement of a solid in an incompressible perfect fluid as a geodesic flow |
| topic | Analysis of PDEs 76B99, 74F10 |
| url | https://arxiv.org/abs/1102.1380 |