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

Anna Amirdjanova; Jie Xiong

doi:10.3934/dcdsb.2006.6.651

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2006, Volume 6, Issue 4: 651-666. Doi: 10.3934/dcdsb.2006.6.651

This issue Previous Article Preface Next Article Pathwise non-exponential decay rates of solutions of scalar nonlinear stochastic differential equations

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
2.
Department of Mathematics, University of Tennessee, 121 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1300

Received: February 2005

Revised: September 2005

Published: July 2006

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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.

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Mathematics Subject Classification: Primary: 60F10, 60H15; Secondary: 60K40.

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