2021/06/16 by Alexei Ilyin, Anna Kostianko, Sergey Zelik · 17 citations
Engineering · Mathematics · #Attractor #Backward Euler method #Boundary (topology) #Bounded function #Dimension (graph theory) #Dirichlet boundary condition #Domain (mathematical analysis) #Euler equations #Euler's formula #Fluid Dynamics and Turbulent Flows #Fractal #Fractal dimension #Geometry #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Pure mathematics #Regularization (linguistics) #Stability and Controllability of Differential Equations #Torus #math.AP #msc:35B40 #msc:35B45 #msc:35L70
paper · pdf · doi:10.1016/j.physd.2022.133156
published in Physica D Nonlinear Phenomena 432, 133156 (Elsevier BV)
arxiv created 2021/06/16 · openalex publication_date 2022/01/28 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dependence of the fractal dimension of global attractors for the damped 3D Euler--Bardina equations on the regularization parameter α>0 and Ekman damping coefficient γ>0 is studied. We present explicit upper bounds for this dimension for the case of the whole space, periodic boundary conditions, and the case of bounded domain with Dirichlet boundary conditions. The sharpness of these estimates when α→0 and γ→0 (which corresponds in the limit to the classical Euler equations) is demonstrated on the 3D Kolmogorov flows on a torus.