Inviscid limit of stochastic damped 2D Navier-Stokes equations

2012/12/03 by H. Bessaih, Bessaih, H., B. Ferrario +1
Mathematics · #35Q35 #60G10 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35Q35 #msc:60G10 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1212.0509

arxiv created 2013/07/29 · arxiv updated 2013/07/30

Abstract

We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The rates are computed with respect to a limit measure of the unique invariant measure of the stochastic damped Navier-Stokes equations.

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