caa a22 4500 467892369 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10955-005-8084-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8084-9 Kuksin Sergei Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, Scotland, UK aut Remarks on the Balance Relations for the Two-Dimensional Navier-Stokes Equation with Random Forcing [Elektronische Daten] [Sergei Kuksin] 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 ξ(t,x) of a stationary solution has a finite exponential moment, and that for any $$a\in{\mathbb R},\,t\geq 0$$ 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. Springer Science + Business Media, Inc., 2006 Two-dimensional Navier-Stokes equation nationallicence stationary measure nationallicence vorticity nationallicence balance relations nationallicence exponential moment nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/1(2006-01-01), 101-114 0022-4715 122:1<101 2006 122 10955 https://doi.org/10.1007/s10955-005-8084-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8084-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kuksin Sergei Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, Scotland, UK aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/1(2006-01-01), 101-114 0022-4715 122:1<101 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer