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

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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

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

Abstract
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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 & Continuous Dynamical Systems - B, 2006, 6 (4) : 651-666. doi: 10.3934/dcdsb.2006.6.651

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