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 differential equations. Since our desire is to
make the core ideas clear, we will mostly work with a specific example: the
stochastically forced Navier Stokes equations. To further clarify ideas, we
will also examine in detail a toy problem. A few general theorems are given.
Spatial regularity, ergodicity, exponential mixing, coupling for a SPDE, and
hypoellipticity are all discussed.Comment: Corrected version of Journees Equations aux derivees partielles
paper(June 2003). Original at
http://www.math.sciences.univ-nantes.fr/edpa/2003
