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

DOI10.1134/S1064562421040165zbMath1477.35149OpenAlexW3213959019MaRDI QIDQ2246873

Serguei Zelik, Alexei A. Ilyin, A. G. Kostianko

Publication date: 16 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562421040165

zbMATH Keywords

attractorsfractal dimensionKolmogorov flowsinviscid Euler-Bardina model

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Attractors (35B41) Direct numerical and large eddy simulation of turbulence (76F65) Fractals (28A80) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Related Items (2)

Trajectory attractors for 3D damped Euler equations and their approximation ⋮ Estimates for the dimension of attractors of a regularized Euler system with dissipation on the sphere

Cites Work

• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• An \(L^ p\) bound for the Riesz and Bessel potentials of orthonormal functions
• Infinite-dimensional dynamical systems in mechanics and physics.
• Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations
• Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations
• Magnetic Lieb–Thirring inequality for periodic functions
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