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Mosc. Math. J., 2003, Volume 3, Number 2, Pages 263–272 (Mi mmj88)  

This article is cited in 7 scientific papers (total in 7 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

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.

Full text: http://www.ams.org/.../abst3-2-2003.html
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 76X05, 35Q99
Received: June 27, 2002
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
\Bibitem{Bog03}
\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
\mathnet{http://mi.mathnet.ru/mmj88}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025262}
\zmath{https://zbmath.org/?q=an:1056.76020}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bogoyavlenskij O., Fuchssteiner B., “Exact MHD solutions with crystallographic symmetries and non-interacting Fourier modes”, Phys. Lett. A, 331:1-2 (2004), 53–59  crossref  mathscinet  zmath  adsnasa  isi
    2. Khomasuridze N., “On some stationary mathematical models for Tornados and other funnel-shaped rotating liquid and gas media”, ZAMM Z. Angew. Math. Mech., 89:1 (2009), 19–27  crossref  mathscinet  zmath  isi  elib
    3. R. S. Saks, “Cauchy problem for the Navier–Stokes equations, Fourier method”, Ufa Math. Journal, 3:1 (2011), 51–77  mathnet  zmath
    4. Fre P., Sorin A.S., “Classification of Arnold-Beltrami Flows and Their Hidden Symmetries”, Phys. Part. Nuclei, 46:4 (2015), 497–632  crossref  isi  elib
    5. Fre P., Grassi P.A., Ravera L., Trigiante M., “Minimal D=7 Supergravity and the Supersymmetry of Arnold-Beltrarni Flux Branes”, J. High Energy Phys., 2016, no. 6, 018  crossref  isi
    6. Fre P., “Supersymmetric M2-Branes With Englert Fluxes, and the Simple Group Psl(2,7)”, Fortschritte Phys.-Prog. Phys., 64:6-7 (2016), 425–462  crossref  isi
    7. Ershkov S.V., “Non-Stationary Creeping Flows For Incompressible 3D Navier-Stokes Equations”, Eur. J. Mech. B-Fluids, 61:1 (2017), 154–159  crossref  isi
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