Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics

Journal Article

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-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.

Full Text

Duke Authors

Cited Authors

  • Mattingly, JC

Published Date

  • November 1, 2002

Published In

Volume / Issue

  • 230 / 3

Start / End Page

  • 421 - 462

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/s00220-002-0688-1

Citation Source

  • Scopus