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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 57–60
DOI: https://doi.org/10.31857/S2686954320020277
(Mi danma50)
 

MATHEMATICS

Attractors of an autonomous model of nonlinear viscous fluid

V. G. Zvyagin, M. V. Kaznacheev

Voronezh State University, Voronezh, Russian Federation
References:
Abstract: For an autonomous model of the motion of a nonlinear viscous fluid, we study the limiting behavior of its weak solutions as time tends to infinity. Namely, the existence of weak solutions on the positive half-axis is established, the trajectory space corresponding to the solutions of this model is determined, and the existence of a minimum trajectory attractor and, then, a global attractor in the phase space is proved using the theory of trajectory spaces. Thus, it turns out that whatever the initial state of the system describing the model is, it is “forgotten” over time and the global attractor is infinitely approached.
Keywords: attractors, trajectory space, nonlinear viscous fluid.
Funding agency Grant number
Russian Science Foundation 19–11–00146
This work was supported by the Russian Science Foundation, project no. 19-11-00146.
Presented: E. I. Moiseev
Received: 27.06.2019
Revised: 27.06.2019
Accepted: 24.01.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 126–128
DOI: https://doi.org/10.1134/S1064562420020271
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. G. Zvyagin, M. V. Kaznacheev, “Attractors of an autonomous model of nonlinear viscous fluid”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 57–60; Dokl. Math., 101:2 (2020), 126–128
Citation in format AMSBIB
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\by V.~G.~Zvyagin, M.~V.~Kaznacheev
\paper Attractors of an autonomous model of nonlinear viscous fluid
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 491
\pages 57--60
\mathnet{http://mi.mathnet.ru/danma50}
\crossref{https://doi.org/10.31857/S2686954320020277}
\zmath{https://zbmath.org/?q=an:1477.35040}
\elib{https://elibrary.ru/item.asp?id=42860663}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 2
\pages 126--128
\crossref{https://doi.org/10.1134/S1064562420020271}
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