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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 499, Pages 13–16
DOI: https://doi.org/10.31857/S2686954321040160 (Mi danma183) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Sharp dimension estimates for the attractors of the regularized damped Euler system

S. V. Zelikab, A. A. Ilyinc, A. G. Kostyankob

a Department of Mathematics, University of Surrey, Guildford, United Kingdom
b School of Mathematics and Statistics, Lanzhou University, Lanzhou, China
c Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954321040160
Abstract: A regularized damped Euler system in two-dimensional and three-dimensional setting is considered. The existence of a global attractor is proved and explicit estimates of its fractal dimension are given. In the case of periodic boundary conditions both in two-dimensional and three-dimensional cases, it is proved that the obtained upper bounds are sharp in the limit a→0+, where a is the parameter describing smoothing of the vector field in the nonlinear term.
Keywords: inviscid Euler–Bardina model, attractors, fractal dimension, Kolmogorov flows.
Presented: B. N. Chetverushkin
Received: 14.05.2021
Revised: 04.06.2021
Accepted: 04.06.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 1, Pages 169–172
DOI: https://doi.org/10.1134/S1064562421040165
Bibliographic databases:
Document Type: Article
UDC: 517.957, 517.984
Language: Russian
Citation: S. V. Zelik, A. A. Ilyin, A. G. Kostyanko, “Sharp dimension estimates for the attractors of the regularized damped Euler system”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 13–16; Dokl. Math., 104:1 (2021), 169–172
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/danma/v499/p13
    • This publication is cited in the following 2 articles:
    1. S. V. Zelik, A. A. Ilyin, A. G. Kostyanko, “Estimates for the Dimension of Attractors of a Regularized Euler System with Dissipation on the Sphere”, Math. Notes, 111:1 (2022), 47–57  mathnet  mathnet  crossref  crossref  mathscinet  isi  scopus
    2. A. Ilyin, A. Kostianko, S. Zelik, “Trajectory attractors for 3D damped Euler equations and their approximation”, Discrete and Continuous Dynamical Systems-S, 15:8 (2022), 2275  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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    Full-text PDF :30
    References:24
     
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