Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 651 - 666, Volume 6, Issue 4, July 2006      doi:10.3934/dcdsb.2006.6.651

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Anna Amirdjanova - Department of Statistics, University of Michigan, 439 West Hall, 1085 S. University Ave., Ann Arbor, MI 48109-1107, United States (email)
Jie Xiong - Department of Mathematics, University of Tennessee, 121 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1300, United States (email)

Abstract: 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:  Large deviation principle, stochastic Navier-Stokes equation, vorticity, exponential tightness.
Mathematics Subject Classification:  Primary: 60F10, 60H15; Secondary: 60K40.

Received: February 2005;      Revised: September 2005;      Available Online: April 2006.