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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 259, Pages 134–142 (Mi tm573)  
This article is cited in 8 scientific papers (total in 8 papers)

Eulerian Limit for 2D Navier–Stokes Equation and Damped/Driven KdV Equation as Its Model

S. B. Kuksinab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Department of Mathematics, Heriot Watt University
Full-text PDF (195 kB) Citations (8)
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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.
Received in December 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 259, Pages 128–136
DOI: https://doi.org/10.1134/S0081543807040098
Bibliographic databases:
Language: English
Citation: S. B. Kuksin, “Eulerian Limit for 2D Navier–Stokes Equation and Damped/Driven KdV Equation as Its Model”, Analysis and singularities. Part 2, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 259, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 134–142; Proc. Steklov Inst. Math., 259 (2007), 128–136
Citation in format AMSBIB
\Bibitem{Kuk07}
\by S.~B.~Kuksin
\paper Eulerian Limit for 2D Navier--Stokes Equation and Damped/Driven KdV Equation as Its Model
\inbook Analysis and singularities. Part~2
\bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 259
\pages 134--142
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm573}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2433681}
\zmath{https://zbmath.org/?q=an:1161.35461}
\elib{https://elibrary.ru/item.asp?id=9572732}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 259
\pages 128--136
\crossref{https://doi.org/10.1134/S0081543807040098}
\elib{https://elibrary.ru/item.asp?id=13565182}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849147161}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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