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Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System

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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 \(\alpha \to {{0}^{ + }}\), where α is the parameter describing smoothing of the vector field in the nonlinear term.

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Authors and Affiliations

  1. Department of Mathematics, University of Surrey, Guildford, United Kingdom

    S. V. Zelik

  2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

    S. V. Zelik & A. G. Kostianko

  3. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. A. Ilyin

Authors
  1. S. V. Zelik
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  2. A. A. Ilyin
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  3. A. G. Kostianko
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Correspondence to S. V. Zelik, A. A. Ilyin or A. G. Kostianko.

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Zelik, S.V., Ilyin, A.A. & Kostianko, A.G. Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System. Dokl. Math. 104, 169–172 (2021). https://doi.org/10.1134/S1064562421040165

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  • DOI: https://doi.org/10.1134/S1064562421040165

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