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Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations |
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| Authors: | Igor Chueshov Annie Millet |
| Institution: | 1. Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody Square, 61077, Kharkov, Ukraine 2. Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris 6-Paris 7, Bo?te Courrier 188, 4 place Jussieu, 75252, Paris Cedex 05, France 3. SAMOS-MATISSE, Centre d’économie de la Sorbonne, Université Paris 1 Panthéon Sorbonne, 90 Rue de Tolbiac, 75634, Paris Cedex 13, France |
| Abstract: | We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also some shell models of turbulence. We state the existence and uniqueness theorem for the class considered. Our main result is a Wentzell-Freidlin type large deviation principle for small multiplicative noise which we prove by a weak convergence method. |
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