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| HAL : hal-00676454, version 1 |
| arXiv : 1203.0417 |
| DOI : 10.1007/s00440-013-0490-3 |
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| Probability Theory and Related Fields (2013) 22 pages |
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| Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise |
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| Arnaud Debussche 1, 2Marco Romito 3 |
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| (2013) |
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| We prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic Navier-Stokes equations in dimension 3. In particular, under very mild assumptions on the noise, we prove that finite dimensional projections of the solutions have densities with respect to the Lebesgue measure which have some smoothness when measured in a Besov space. This is proved thanks to a new argument inspired by an idea introduced in Fournier and Printems (2010). |
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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 : | Dipartimento di Matematica "Ulisse Dini" |
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University of Firenze |
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| Analyse numérique Processus stochastiques |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Equations aux dérivées partielles Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Probability – Mathematical Physics – Analysis of PDEs |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1203.0417 |
| hal-00676454, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00676454 | |
| oai:hal.archives-ouvertes.fr:hal-00676454 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Lundi 5 Mars 2012, 13:58:26 | |
| Dernière modification le : Lundi 10 Juin 2013, 16:08:27 | |
