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July  2006, 6(4): 651-666. doi: 10.3934/dcdsb.2006.6.651

Large deviation principle for a stochastic navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow

Anna Amirdjanova 1, and  Jie Xiong 2,

1. 

Department of Statistics, University of Michigan, 439 West Hall, 1085 S. University Ave., Ann Arbor, MI 48109-1107, United States
2. 

Department of Mathematics, University of Tennessee, 121 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1300, United States

Received  February 2005 Revised  September 2005 Published  April 2006

We derive a large deviation principle for a stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid when the magnitude of the random term tends to zero. The key is the verification of the exponential tightness for the stochastic vorticity.
Keywords: vorticity, stochastic Navier-Stokes equation, exponential tightness., Large deviation principle.
Mathematics Subject Classification: Primary: 60F10, 60H15; Secondary: 60K4.
Citation: Anna Amirdjanova, Jie Xiong. Large deviation principle for a stochastic navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 651-666. doi: 10.3934/dcdsb.2006.6.651
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