Geodesic
Sharp dimension estimates for the attractors of the regularized damped Euler system
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 13-16

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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 $a\to0^+$, 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. 
@article{DANMA_2021_499_a2,
     author = {S. V. Zelik and A. A. Ilyin and A. G. Kostyanko},
     title = {Sharp dimension estimates for the attractors of the regularized damped {Euler} system},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {13--16},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_499_a2/}
}
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S. V. Zelik; A. A. Ilyin; A. G. Kostyanko. Sharp dimension estimates for the attractors of the regularized damped Euler system. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 13-16. http://geodesic.mathdoc.fr/item/DANMA_2021_499_a2/