Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations

M Hairer, JC Mattingly, M Scheutzow - Probability theory and related fields, 2011 - Springer
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 …

Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations

M Hairer, JC Mattingly - 2008 - projecteuclid.org
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 …

On recent progress for the stochastic Navier Stokes equations

J Mattingly - Journées Equations aux dérivées partielles, 2003 - numdam.org
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 …

Probabilistic well-posedness for the cubic wave equation

N Burq, N Tzvetkov - Journal of the European Mathematical Society, 2013 - ems.press
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 …

Almost-sure exponential mixing of passive scalars by the stochastic Navier–Stokes equations

J Bedrossian, A Blumenthal… - The Annals of …, 2022 - projecteuclid.org
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 …

Ergodicity results for the stochastic Navier–Stokes equations: an introduction

P Constantin, A Debussche, GP Galdi… - Topics in Mathematical …, 2013 - Springer
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 …

Existence and regularity of invariant measures for the three dimensional stochastic primitive equations

N Glatt-Holtz, I Kukavica, V Vicol… - Journal of Mathematical …, 2014 - pubs.aip.org
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 …

On unique ergodicity in nonlinear stochastic partial differential equations

N Glatt-Holtz, JC Mattingly, G Richards - Journal of Statistical Physics, 2017 - Springer
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

P Constantin, N Glatt-Holtz, V Vicol - Communications in Mathematical …, 2014 - Springer
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 …

[HTML][HTML] Well-posedness and stationary solutions of McKean-Vlasov (S) PDEs

L Angeli, J Barré, M Kolodziejczyk, M Ottobre - Journal of Mathematical …, 2023 - Elsevier
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 …