There are many Markov chains on infinite dimensional spaces whose one-step transition
kernels are mutually singular when starting from different initial conditions. We give results …

We develop a general method to prove the existence of spectral gaps for Markov
semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for …

We give an overview of the ideas central to some recent developments in the ergodic theory
of the stochastically forced Navier Stokes equations and other dissipative stochastic partial …

The purpose of this article is to introduce for dispersive partial differential equations with
random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We …

We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of
the stochastically-forced 2D Navier–Stokes equations and 3D hyper-viscous Navier–Stokes …

The theory of the stochastic Navier–Stokes equations (SNSE) has known a lot of important
advances those last 20 years. Existence and uniqueness have been studied in various …

We establish the continuity of the Markovian semigroup associated with strong solutions of
the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The …

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive
framework for proving the uniqueness of invariant measures for a variety of stochastic partial …

Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations Page 1
Digital Object Identifier (DOI) 10.1007/s00220-014-2003-3 Commun. Math. Phys. 330, 819–857 …

This paper is composed of two parts. In the first part we consider McKean-Vlasov Partial
Differential Equations (PDEs), obtained as thermodynamic limits of interacting particle …