## Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics (2002)

Citations: | 33 - 9 self |

### BibTeX

@MISC{Mattingly02exponentialconvergence,

author = {Jonathan C. Mattingly},

title = {Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics},

year = {2002}

}

### OpenURL

### Abstract

We prove that the two dimensional Navier-Stokes equations possesses an exponentially attracting invariant measure. This result is in fact the consequence of a more general "Harris-like" ergodic theorem applicable to many dissipative stochastic PDEs and stochastic processes with memory. A simple iterated map example is also presented to help build intuition and showcase the central ideas in a less encumbered setting. To analyze the iterated map, a general "Doeblin-like" theorem is proven. One of the main features of this paper is the novel coupling construction used to examine the ergodic theory of the non-Markovian processes.