The Eulerian limit for 2D statistical hydrodynamics

Sergei B. Kuksin

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


We consider the 2D Navier-Stokes system, perturbed by a white in time random force, proportional to the square root of the viscosity. We prove that under the limit "time to infinity, viscosity to zero" each of its (random) solution converges in distribution to a non-trivial stationary process, formed by solutions of the (free) Euler equation, while the Reynolds number grows to infinity. We study the convergence and the limiting solutions.

Original languageEnglish
Pages (from-to)469-492
Number of pages24
JournalJournal of Statistical Physics
Issue number1-2
Publication statusPublished - Apr 2004


  • 2D Euler equation
  • 2D Navier-Stokes equation
  • 2D turbulence
  • Invariant measure
  • Random force
  • Reynolds number
  • Stationary measure
  • White noise


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