Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

S. B. Kuksin

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures. © 2007 Pleiades Publishing, Ltd.

Original languageEnglish
Pages (from-to)128-136
Number of pages9
JournalProceedings of the Steklov Institute of Mathematics
Volume259
Issue number2
DOIs
Publication statusPublished - Dec 2007

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