Remarks on the balance relations for the two-dimensional navier-stokes equation with random forcing

Abstract

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ?(t,x) of a stationary solution has a finite exponential moment, and that for any a ? R, t=0 the expectation of the integral of |dx?| over the level-set {x|?(t,x)=a}, up to a constant factor equals the expectation of the integral of |dx?| over the same set. © 2006 Springer Science + Business Media, Inc.</p