Andrei Agrachev, Sergei Kuksin, Andrey Sarychev, Armen Shirikyan
On finite-dimensional projections of distributions for solutions of randomly forced PDE's
(483K, Postscript)

ABSTRACT.  The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension.