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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

Abstract:

 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.

Keywords

Stochastic Process Invariant Measure Ergodic Theory Central Idea Ergodic Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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