05-116 Sergei B. Kuksin
Remarks on the balance relations for the two-dimensional Navier--Stokes equation with random forcing. (1557K, post-script) Mar 24, 05
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 05-116.src( 05-116.keywords , new.ps )