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”, Mat. Zametki, 2022, Volume 111, Issue 1,Pages <nobr>54

This article is cited in 2 papers

Estimates for the Dimension of Attractors of a Regularized Euler System with Dissipation on the Sphere

S. V. Zelik^abc, A. A. Ilyin^cd, A. G. Kostyanko^e

^a University of Surrey
^b Lanzhou University
^c Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
^d University of Science and Technology "Sirius", Sochi
^e Imperial College London

Abstract: We prove the existence of a global attractor of a regularized Euler–Bardina system with dissipation on the two-dimensional sphere and in arbitrary domains on the sphere. Explicit estimates for the fractal dimension of the attractor in terms of its physical parameters are obtained.

Keywords: Euler's system, Bardina's model, attractors, fractal dimension, spectral inequalities on the sphere.

UDC: 517.957+517.984

Received: 21.07.2021

DOI: 10.4213/mzm13231