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

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 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.

References in corpus (3)

• Large deviations for infinite dimensional stochastic dynamical systems
• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
• Large deviations for the Boussinesq Equations under Random Influences

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