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| HAL : hal-00605082, version 1 |
| arXiv : 1104.4754 |
| DOI : 10.1088/0951-7715/25/7/2093 |
| Fiche détaillée |  Récupérer au format |
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| Nonlinearity 25, 7 (2012) 2093-2118 |
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| Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise |
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| Arnaud Debussche 1, 2Nathan Glatt-Holtz 3 |
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| (2012) |
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| The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2 : | IPSO (INRIA - IRMAR) |
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CNRS : UMR6074 – INRIA – Université de Rennes 1 |
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| 3 : | Department of mathematics [Bloomington] |
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Indiana University |
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| 4 : | Institute for Scientific Computing and Applied Mathematics (ISC) |
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Indiana University |
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| Analyse numérique Processus stochastiques |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Probabilités |
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| Navier-Stokes equations – Large-scale ocean – Dynamics equations – Pathwise solutions – well-posedness – backscatter – martingale – system – space |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1104.4754 |
| hal-00605082, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00605082 | |
| oai:hal.archives-ouvertes.fr:hal-00605082 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Jeudi 30 Juin 2011, 15:07:59 | |
| Dernière modification le : Lundi 25 Février 2013, 13:15:31 | |
