Stochastic 2D hydrodynamical type systems: Well posedness and large deviations

Igor Chueshov (1) , Annie Millet (2, 3)

1 Department of Mechanics and Mathematics
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

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 2D magnetic Bénard problem and also some shell models of turbulence. We first prove 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 weak convergence method.

Mots clés: Hydrodynamical models; MHD; Bénard convection; shell models of turbulence; stochastic PDEs; large deviations

Domaines: Probabilités [math.PR]

Igor Chueshov, Annie Millet. Stochastic 2D hydrodynamical type systems: Well posedness and large deviations. Applied Mathematics and Optimization, 2010, 61 (3), pp.379-420. ⟨10.1007/s00245-009-9091-z⟩. ⟨hal-00295023v3⟩