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Multi-vortices and Lower Bounds for the Attractor Dimension of 2D Navier–Stokes Equations

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Abstract

A new method for obtaining lower bounds for the dimension of attractors for the Navier–Stokes equations is presented, which does not use Kolmogorov flows. By applying this method, exact estimates of the dimension are obtained for the case of equations on a plane with Ekman damping. Similar estimates were previously known only for the case of periodic boundary conditions. In addition, similar lower bounds are obtained for the classical Navier–Stokes system in a two-dimensional bounded domain with Dirichlet boundary conditions.

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Funding

This work was supported by the Russian Science Foundation, project no. 23-71-30008.

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Correspondence to A. G. Kostianko, A. A. Ilyin, D. Stone or S. V. Zelik.

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The authors of this work declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Kostianko, A.G., Ilyin, A.A., Stone, D. et al. Multi-vortices and Lower Bounds for the Attractor Dimension of 2D Navier–Stokes Equations. Dokl. Math. 109, 179–182 (2024). https://doi.org/10.1134/S1064562424702016

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  • DOI: https://doi.org/10.1134/S1064562424702016

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