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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 512, Pages 42–46
DOI: https://doi.org/10.31857/S2686954322600549 (Mi danma396) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On asymptotics of attractors to Navier–Stockes system in anisotropic medium with small periodic obstacles

K. A. Bekmaganbetovab, A. M. Toleubaibc, G. A. Chechkinbde

a Kazakhstan Branch of Lomonosov Moscow State University, Nur-Sultan, Astana, Kazakhstan
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty, Kazakhstan
c Eurasian National University named after L.N. Gumilyov, Astana, Kazakhstan
d Lomonosov Moscow State University, Moscow, Russian Federation
e Institute of Mathematics with Computing Centre – Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russian Federation
Citations (1)
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DOI: https://doi.org/10.31857/S2686954322600549
Abstract: The paper considers a two-dimensional system of Navier–Stokes equations in medium with anisotropic variable viscosity and periodic small obstacles. It is proved that the trajectory attractors of this system tend in a certain weak topology to the trajectory attractors of the averaged system of Navier–Stokes equations with an additional potential in a medium without obstacles.
Keywords: attractors, averaging, system of equations Navier–Stokes, nonlinear equations, weak convergence, perforated region, rapidly oscillating terms, anisotropic medium.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP14869553
Moscow Center of Fundamental and Applied Mathematics 075-15-2022-284
The research presented in Section 2 was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, grant AR14869553. The third author’s work presented in Section 3 was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2022-284.
Presented: V. V. Kozlov
Received: 07.09.2022
Revised: 20.05.2023
Accepted: 25.05.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 1, Pages 277–281
DOI: https://doi.org/10.1134/S1064562423700813
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: K. A. Bekmaganbetov, A. M. Toleubai, G. A. Chechkin, “On asymptotics of attractors to Navier–Stockes system in anisotropic medium with small periodic obstacles”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 42–46; Dokl. Math., 108:1 (2023), 277–281
Citation in format AMSBIB
\Bibitem{BekTolChe23}
\by K.~A.~Bekmaganbetov, A.~M.~Toleubai, G.~A.~Chechkin
\paper On asymptotics of attractors to Navier--Stockes system in anisotropic medium with small periodic obstacles
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 512
\pages 42--46
\mathnet{http://mi.mathnet.ru/danma396}
\crossref{https://doi.org/10.31857/S2686954322600549}
\elib{https://elibrary.ru/item.asp?id=54538833}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 1
\pages 277--281
\crossref{https://doi.org/10.1134/S1064562423700813}
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