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On finitedimensional projections of distributions for solutions of randomly forced PDE's
 

Summary: On finite­dimensional projections of distributions
for solutions of randomly forced PDE's
Sur les projections de dimension finie des
distributions pour les solutions d'EDP avec une
perturbation al’eatoire
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 finite­dimensional analytic maps. We establish
su#cient 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.
L'article est consacr’e ‘a l'’etude de l'image des mesures de probabilit’e
sur un espace hilbertien par des applications analytiques de dimension
finie. On ’etablit des conditions su#santes sous lesquelles l'image d'une
mesure poss‘ede une densit’e par rapport ‘a la mesure de Lebesgue et
d’epend contin“ument de l'application. Les r’esultats obtenus s'appliquent
aux ’equations de Navier--Stokes 2D perturb’ees par diverses forces al’eatoires
de dimension peu ’elev’ee.

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Kuksin, Sergei B. - Department of Mathematics, Heriot-Watt University

 

Collections: Engineering; Mathematics