Ergodicity for the randomly forced 2D Navier-Stokes equations

Sergei Kuksin, Armen Shirikyan

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

We study space-periodic 2D Navier-Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N0 coefficients (where N0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties. © 2001 Kluwer Academic Publishers.

Original languageEnglish
Pages (from-to)147-195
Number of pages49
JournalMathematical Physics, Analysis and Geometry
Volume4
Issue number2
DOIs
Publication statusPublished - 2001

Keywords

  • Kick-force
  • Navier-Stokes equations
  • Random dynamical system
  • Ruelle-Perron-Frobenius theorem
  • Stationary measure

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