Dimension estimates for the attractor of the regularized damped Euler equations on the sphere

2021/07/22 by Alexei Ilyin, Ilyin, Alexei, Anna Kostianko +3 · 1 citation
Computer Science · Engineering · Mathematics · #35B40 #35B45 #35L70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Spectral Theory (math.SP) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.10779

openalex publication_date 2021/07/22 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28

Abstract

We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of its fractal dimension in terms of the physical parameters.

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• Attractor of the limiting Navier--Stokes--Voigt system in \mathbb R⁴

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