On finite-dimensional projections of distributions for solutions of   randomly forced PDE's
  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. 
Andrei Agrachev (SISSA-Isas), Sergei Kuksin (Mathematics Department of   Heriot-Watt University), Andrey Sarychev (DMD), Arm...