Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation

Igor Chueshov, Sergei Kuksin

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


In the thin domain Oe = T2 × (0, e), where T2 is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray a-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit e ? 0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure µ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in Oe, when e « 1. © 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)1352-1367
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Issue number10-12
Publication statusPublished - 15 Jul 2008


  • 3D Navier-Stokes equations
  • Ergodicity
  • Leray α-model
  • Stationary measure
  • Thin domains
  • White noise


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