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

被引：166

作者：

Chueshov, Igor ^{[1
,2
]}

Millet, Annie ^{[3
]}

机构：

[1] Univ Paris 07, Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

[2] Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine

[3] Univ Paris 01, SAMOS MATISSE, Ctr Econ Sorbonne, F-75634 Paris 13, France

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2010年 / 61卷 / 03期

关键词：

Hydrodynamical models; MHD; Benard convection; Shell models of turbulence; Stochastic PDEs; Large deviations; NAVIER-STOKES EQUATIONS; MULTIPLICATIVE NOISE; EVOLUTION EQUATIONS; MODEL; TURBULENCE; DIMENSION; EXISTENCE; FLUID; SPACE;

D O I：

10.1007/s00245-009-9091-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 B,nard 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.

引用

页码：379 / 420

页数：42

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