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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
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
Citation:
O. I. Bogoyavlenskii, “Infinite families of exact periodic solutions to the Navier–Stokes equations”, Mosc. Math. J., 3:2 (2003), 263–272
Linking options:
https://www.mathnet.ru/eng/mmj88 https://www.mathnet.ru/eng/mmj/v3/i2/p263
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Abstract page: | 336 | References: | 71 |
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