On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations

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\u2013Stokes equations perturbed by various random forces of low dimension

Passive tracer in a flow corresponding to a two dimensional stochastic Navier Stokes equations

In this paper we prove the law of large numbers and central limit theorem for trajectories of a particle carried by a two dimensional Eulerian velocity field. The field is given by a solution of a stochastic Navier--Stokes system with a non-degenerate noise. The spectral gap property, with respect to Wasserstein metric, for such a system has been shown in [9]. In the present paper we show that a similar property holds for the environment process corresponding to the Lagrangian observations of the velocity. In consequence we conclude the law of large numbers and the central limit theorem for the tracer. The proof of the central limit theorem relies on the martingale approximation of the trajectory process

Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises

International audienceWe prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Kolmogorov equation approach

On Random Attractors for Mixing Type Systems

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system