On Recent Progress for the Stochastic Navier Stokes Equations
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2004
 DOI:
 10.48550/arXiv.math/0409194
 arXiv:
 arXiv:math/0409194
 Bibcode:
 2004math......9194M
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Dynamical Systems;
 Mathematics  Mathematical Physics;
 37A25;
 37A60;
 37N10;
 37L55;
 76F55;
 76F20;
 60H15;
 60H07;
 35R60
 EPrint:
 Corrected version of Journees Equations aux derivees partielles paper(June 2003). Original at http://www.math.sciences.univnantes.fr/edpa/2003/