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Applied Mathematics and Optimization

, Volume 61, Issue 3, pp 379–420 | Cite as

Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations

  • Igor Chueshov
  • Annie MilletEmail author
Article

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.

Hydrodynamical models MHD Bénard convection Shell models of turbulence Stochastic PDEs Large deviations 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsKharkov National UniversityKharkovUkraine
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversités Paris 6-Paris 7, Boîte Courrier 188Paris Cedex 05France
  3. 3.SAMOS-MATISSE, Centre d’Économie de la SorbonneUniversité Paris 1 Panthéon SorbonneParis Cedex 13France

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