Sergei B. Kuksin
Remarks on the balance relations for the two-dimensional
Navier--Stokes equation with random forcing.
(1557K, post-script)
ABSTRACT. We use the balance relations for the stationary in time solutions of
the randomly forced 2D Navier-Stokes equations, found by Kuksin-Penrose
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 level-set $\{x\mid\xi(t,x)=a\}$, up to a
constant factor equals the expectation of the integral of
$|\nabla_x\xi|^{-1}$ over the same set.