Gibbsian dynamics and invariant measures for stochastic dissipative PDEs

E. Weinan, Di Liu

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1125-1156
Number of pages32
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Ergodicity
  • Infinite-dimensional random dynamical systems
  • Invariant measures
  • Stationary processes
  • Stochastic partial differential equations


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