On finite-dimensional projections of distributions for solutions of randomly forced PDE's

Details On finite-dimensional projections of distributions for solutions of randomly forced PDE's On finite-dimensional projections of distributions for solutions of randomly forced PDE's

2006-03-13

arxiv.org/abs/math/0603295v1

Annales de l\'Institut Henri Poincare (B) Probability and Statistics 43, (2007) 399-415

Mathematics

Analysis of PDEs

24 pages

Scientific paper

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.

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