Communications in Mathematical Physics

, Volume 224, Issue 1, pp 83–106 | Cite as

Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation

  • Weinan E
  • J. C. Mattingly
  • Ya. Sinai
Article

Abstract:

We study stationary measures for the two-dimensional Navier–Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all “determining modes” are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Weinan E
    • 1
  • J. C. Mattingly
    • 2
  • Ya. Sinai
    • 3
  1. 1.Department of Mathematics and Program in Applied and Computational MathematicsPrinceton University and School of Mathematics, Peking University, Beijing, P.R. ChinaPrincetonUSA
  2. 2.Department of Mathematics, Stanford UniversityStanfordUSA
  3. 3.Department of Mathematics, Princeton University and Landau Institute of Theoretical Physics, Moscow, RussiaPrincetonUSA

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