The theoretical study of the self-organization of two-dimensional and geophysical turbulent
flows is addressed based on statistical mechanics methods. This review is a self-contained …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

Now back in print by the AMS, this is a significantly revised edition of a book originally
published in 1987 by Academic Press. This book gives the reader an introduction to the …

This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are
studied. We characterize the smallest closed invariant subspace for this model and show …

This book is dedicated to the mathematical study of two-dimensional statistical
hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random …

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 …

We prove that the two dimensional Navier-Stokes equations possess an exponentially
attracting invariant measure. This result is in fact the consequence of a more general``Harris …

We consider parabolic stochastic partial differential equations driven by white noise in time.
We prove exponential convergence of the transition probabilities towards a unique invariant …

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic
stochastic PDEs with" polynomial" nonlinearities and additive noise, considered as abstract …