On Recent Progress for the Stochastic Navier Stokes Equations

Details On Recent Progress for the Stochastic Navier Stokes Equations On Recent Progress for the Stochastic Navier Stokes Equations

2004-09-11

arxiv.org/abs/math/0409194v1

See http://www.math.sciences.univ-nantes.fr/edpa/2003/

Mathematics

Probability

Corrected version of Journees Equations aux derivees partielles paper(June 2003). Original at http://www.math.sciences.univ-

Scientific paper

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.

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