Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Sritharan, S. S. ; Sundar, P.

关键词: Stochastic Navier-Stokes equations;    large deviations;    Girsanov theorem;   

DOI  :  10.1016/j.spa.2006.04.001

来源: Elsevier

【 摘 要 】

A Wentzell-Freidlin type large deviation principle is established for the two-dimensional Navier-Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The large deviation principle is equivalent to the Laplace principle in our function space setting. Hence, the weak convergence approach is employed to obtain the Laplace principle for solutions of stochastic Navier-Stokes equations. The existence and uniqueness of a strong solution to (a) stochastic Navier-Stokes equations with a small multiplicative noise, and (b) Navier-Stokes equations with an additional Lipschitz continuous drift term are proved for unbounded domains which may be of independent interest. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free