Random kick-forced 3D Navier-Stokes equations in a thin domain

Igor Chueshov, Sergei Kuksin

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We consider the Navier-Stokes equations in the thin 3D domain 2 × (0, e), where 2 is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly, when e ? 1, the equation has a unique stationary measure and, secondly, after averaging in the thin direction this measure converges (as e ? 0) to a unique stationary measure for the Navier-Stokes equation on 2. Thus, the 2D Navier-Stokes equations on surfaces describe asymptotic in time, and limiting in e, statistical properties of 3D solutions in thin 3D domains. © 2007 Springer-Verlag.

Original languageEnglish
Pages (from-to)117-153
Number of pages37
JournalArchive for Rational Mechanics and Analysis
Volume188
Issue number1
DOIs
Publication statusPublished - Apr 2008

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