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

2008/07/31 by Igor Chueshov, Annie Millet · 1 citation
Mathematics · #math.PR #msc:60H15 #msc:60F10 #msc:76D06 #msc:76M35

paper · pdf · doi:10.1007/s00245-009-9091-z

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

arxiv created 2009/09/29 · arxiv updated 2011/12/15

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.

Cited by

• Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type