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

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.

24 pages

Cited by in corpus (13)

• Controllability of the discrete-spectrum Schrodinger equation driven by an external field
• Invariant densities for dynamical systems with random switching
• Exponential mixing for a class of dissipative PDEs with bounded degenerate noise
• A note on Harris' ergodic theorem, controllability and perturbations of harmonic networks
• Controllability implies mixing I. Convergence in the total variation metric
• Approximate controllability for Navier--Stokes equations in $3D$ rectangles under Lions boundary conditions
• Notes on Statistically Invariant States in Stochastically Driven Fluid Flows
• Simultaneous approximate tracking of density matrices for a system of Schroedinger equations
• An Averaging Theorem for Perturbed KdV Equation
• Exponential mixing under controllability conditions for SDEs driven by a degenerate Poisson noise
• Approximate controllability for Navier--Stokes equations in {\rm 3D} Cylinders under Lions boundary conditions by an explicit saturating set
• Exponential mixing of constrained random dynamical systems via controllability conditions
• Existence of a density of the 2Dim Stochastic Navier Stokes Equation driven by Levy processes or fractional Brownian motion