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| HAL : hal-00284725, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Journal de Mathématiques Pures et Appliqués 91, 2 (2009) 137-155 |
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| Generalized solutions for the Euler equations in one and two dimensions |
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| Marc Bernot 1Alessio Figalli 2 |
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| (02/2009) |
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| In this paper we study generalized solutions (in the Brenier's sense) for the Euler equations. We prove that uniqueness holds in dimension one whenever the pressure field is smooth, while we show that in dimension two uniqueness is far from being true. In the case of the two-dimensional disc we study solutions to Euler equations where particles located at a point $x$ go to $-x$ in a time $\pi$, and we give a quite general description of the (large) set of such solutions. As a byproduct, we can construct a new class of classical solutions to Euler equations in the disc. |
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| 1 : | Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) |
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CNRS : UMR5669 – École Normale Supérieure - Lyon |
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| 2 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| 3 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Euler incompressible |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00284725, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00284725 | |
| oai:hal.archives-ouvertes.fr:hal-00284725 | |
| Contributeur : Filippo Santambrogio | |
| Soumis le : Mardi 3 Juin 2008, 15:51:46 | |
| Dernière modification le : Jeudi 12 Février 2009, 17:03:04 | |
