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

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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.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody Square, 61077, Kharkov, Ukraine

    Igor Chueshov

  2. Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris 6-Paris 7, Boîte Courrier 188, 4 place Jussieu, 75252, Paris Cedex 05, France

    Annie Millet

  3. SAMOS-MATISSE, Centre d’Économie de la Sorbonne, Université Paris 1 Panthéon Sorbonne, 90 Rue de Tolbiac, 75634, Paris Cedex 13, France

    Annie Millet

Authors
  1. Igor Chueshov
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  2. Annie Millet
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Correspondence to Annie Millet.

Additional information

The research of the second named author is partially supported by the research project BMF2003-01345.

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Chueshov, I., Millet, A. Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations. Appl Math Optim 61, 379–420 (2010). https://doi.org/10.1007/s00245-009-9091-z

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