 05116 Sergei B. Kuksin
 Remarks on the balance relations for the twodimensional
NavierStokes equation with random forcing.
(1557K, postscript)
Mar 24, 05

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Abstract. We use the balance relations for the stationary in time solutions of
the randomly forced 2D NavierStokes equations, found by KuksinPenrose
in \cite{KP05},
to study these solutions further. We show that the vorticity
$\xi(t,x)$ of a stationary solution has a finite exponential moment,
and that for any $a\in\R,\,t\ge0$ the expectation of the integral of
$\nabla_x\xi$ over the levelset $\{x\mid\xi(t,x)=a\}$, up to a
constant factor equals the expectation of the integral of
$\nabla_x\xi^{1}$ over the same set.
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