Summary: arXiv:math/0603295v1[math.AP]13Mar2006
On finite-dimensional projections of distributions
for solutions of randomly forced PDE's
A. Agrachev 1
, S. Kuksin 2
, A. Sarychev 3
, A. Shirikyan 4
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 Navier­Stokes equations
perturbed by various random forces of low dimension.
AMS subject classifications: 35Q30, 60H15, 93C20
Keywords: 2D Navier­Stokes system, analytic transformations, random
perturbations
Contents
0 Introduction 2
1 Decomposable measures on Hilbert spaces 4

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

Collections: Engineering; Mathematics