Communications in Mathematical Physics

, Volume 230, Issue 3, pp 421–462 | Cite as

Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics

  • Jonathan C. Mattingly


 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.


Stochastic Process Invariant Measure Ergodic Theory Central Idea Ergodic Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jonathan C. Mattingly
    • 1
  1. 1.Department of Mathematics, Stanford University, Stanford, CA 94305, USA. E-mail: jonm@math.stanford.eduUS

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