We study the mixing and dissipation properties of the advection–diffusion equation with
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …

In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity $\kappa $ should display a $| k|^{-1} $ power spectrum along an inertial …

We consider a fluid governed by the randomly forced 2D Navier-Stokes system. It is
assumed that the force is bounded, acts directly only on a small number of Fourier modes …

We study the Lagrangian flow associated to velocity fields arising from various models of
stochastic fluid mechanics. We prove that in many circumstances, these flows are chaotic …

The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems.
In the literature, there are very few results on the irreducibility of stochastic partial differential …

We study the large deviation principle (LDP) for locally damped nonlinear wave equations
perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish …

The purpose of this paper is to establish the Donsker–Varadhan type large deviations
principle (LDP) for the two-dimensional stochastic Navier–Stokes system. The main novelty …

In this paper, we mainly study the turbulence of Lagrangian flow advected by stochastic 2D
Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The …

We continue the investigation, started in Jakšić et al. in (J. Stat. Phys. 166: 926–1015, 2017),
of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We …