Journal of Statistical Physics

, Volume 108, Issue 5–6, pp 1125–1156 | Cite as

Gibbsian Dynamics and Invariant Measures for Stochastic Dissipative PDEs

  • E Weinan
  • Di Liu

Abstract

We present a general strategy for proving ergodicity for stochastically forced nonlinear dissipative PDEs. It consists of two main steps. The first step is the reduction to a finite dimensional Gibbsian dynamics of the low modes. The second step is to prove the equivalence between measures induced by different past histories using Girsanov theorem. As applications, we prove ergodicity for Ginzburg–Landau, Kuramoto–Sivashinsky and Cahn–Hilliard equations with stochastic forcing.

Ergodicity invariant measures stationary processes infinite-dimensional random dynamical systems stochastic partial differential equations 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • E Weinan
    • 1
    • 3
  • Di Liu
    • 2
  1. 1.Department of Mathematics and Program in Applied and Computational MathematicsPrinceton UniversityPrinceton
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrinceton
  3. 3.School of Mathematical SciencesPeking UniversityPeople's Republic of China

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