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| 20/09/2018 | | | | 14h | | | | salles de conférences | | |
| | Nicolas Besse (OCA) | | | | Regularity of the geodesic flow of the incompressible Euler equations on a manifold | | | | In this talk we investigate the regularity in time of the volume-preserving geodesic flow, which is associated with the incompressible Euler equations on a compact d-dimensional Riemannian manifold with boundary. The global regularity for smooth initial data is not only an open issue, but the behaviour of solutions and many pratical applications also depend on complex geometries. This result completes the local-in-time well-posedness theory of Ebin and Marsden (Ann. Math. 92 (1970) 102–163). Indeed, the first result of this talk paper states roughly that the time smoothness of geodesic curves is only limited by the smoothness of the manifold and its boundary, which is measured in a broad ultradifferentiable class, including the real analytic and Gevrey classes. A second result is that our simple constructive proof can be used to design efficient and very high-order semi-Lagrangian methods for integrating accurately the Euler equations on a manifold. Indeed, the proof makes use of a new Lagrangian formulation of Euler equations on d-dimensional manifolds, which is a generalization of the Cauchy invariants equation in $R^3$. This Lagrangian formulation, together with the Lagrangian incompressibility condition and the invariance of the boundary under the Lagrangian flow allow us to derive recursion relations among time-Taylor coefficients of the time-series expansion of the geodesic flow.
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| | Lifeng Zhao, University of Science and Technology of China (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Nicolas Rougerie, Université Grenoble-Alpes (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | José Carillo, Imperial College (London) (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (pont) ??? (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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| | Séminaire Analyse des EDP (organisation D. Chiron, P. Raphaël, financé par l'ERC Singwave) | | | | | | | | | | |
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