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On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations |
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| Authors: | A Agrachev S Kuksin A Sarychev |
| Institution: | a SISSA-ISAS, via Beirut 2-4, Trieste 34014, Italy b Steklov Institute of Mathematics, 8 Gubkina St., 117966 Moscow, Russia c Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK d DiMaD, University of Florence, via C. Lombroso 6/17, Firenze 50134, Italy e Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France |
| 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. |
| Keywords: | 35Q30 60H15 93C20 |
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