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Moscow Mathematical Journal, 2003, Volume 3, Number 2, Pages 263–272
DOI: https://doi.org/10.17323/1609-4514-2003-3-2-263-272 (Mi mmj88) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Infinite families of exact periodic solutions to the Navier–Stokes equations

O. I. Bogoyavlenskiiab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Queen's University
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DOI: https://doi.org/10.17323/1609-4514-2003-3-2-263-272
Abstract: A complete classification of all periodic solutions to the 3-dimensional Navier–Stokes equations with pairwise non-interacting Fourier modes is obtained. The corresponding sets of the wave vectors $k\in\mathbb Z^3$ necessarily belong either to the straight lines, the planes, the circumferences or the spheres. The constructed exact periodic solutions are smooth and exist for all values of the time variable $t>0$.
Key words and phrases: Navier–Stokes equations, periodic solutions, Fourier modes, Beltrami equation.
Received: June 27, 2002
Bibliographic databases:
Document Type: Article
MSC: 76X05, 35Q99
Language: English
Citation: O. I. Bogoyavlenskii, “Infinite families of exact periodic solutions to the Navier–Stokes equations”, Mosc. Math. J., 3:2 (2003), 263–272
Citation in format AMSBIB
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\by O.~I.~Bogoyavlenskii
\paper Infinite families of exact periodic solutions to the Navier--Stokes equations
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 263--272
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\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-263-272}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2025262}
\zmath{https://zbmath.org/?q=an:1056.76020}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208594200001}
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