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

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

2008-07-11

arxiv.org/abs/0807.1810v3

Applied Mathematics and Optimization 61, 3 (2010) 379-420

Mathematics

Probability

Scientific paper

10.1007/s00245-009-9091-z

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 B\'enard 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.

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