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

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-009-9091-Z· OSTI ID:21480265

Chueshov, Igor ^[1]; Millet, Annie ^[2]

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1. Kharkov National University, Department of Mechanics and Mathematics (Ukraine)
2. Universites Paris 6-Paris 7, Boite Courrier 188, Laboratoire de Probabilites et Modeles Aleatoires (France)

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 Benard 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.

• OSTI ID: 21480265
• Journal Information: Applied Mathematics and Optimization, Vol. 61, Issue 3; Other Information: DOI: 10.1007/s00245-009-9091-z; Copyright (c) 2010 Springer Science+Business Media, LLC; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONVERGENCE
MAGNETOHYDRODYNAMICS
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NOISE
NONLINEAR PROBLEMS
STOCHASTIC PROCESSES
TURBULENCE
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS