Trajectory attractors for 3D damped Euler equations and their\n approximation

2021/12/27 by Alexei Ilyin, Ilyin, Alexei, Anna Kostianko +3
Engineering · Mathematics · #35B40 #35B45 #35L70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.13691

openalex publication_date 2021/12/27 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28

Abstract

We study the global attractors for the damped 3D Euler--Bardina equations\nwith the regularization parameter \α>0 and Ekman damping coefficient\n\γ>0 endowed with periodic boundary conditions as well as their damped\nEuler limit \α\→0. We prove that despite the possible non-uniqueness of\nsolutions of the limit Euler system and even the non-existence of such\nsolutions in the distributional sense, the limit dynamics of the corresponding\ndissipative solutions introduced by P. ,Lions can be described in terms of\nattractors of the properly constructed trajectory dynamical system. Moreover,\nthe convergence of the attractors Cal A(\α) of the regularized system to\nthe limit trajectory attractor Cal A(0) as \α\→0 is also established\nin terms of the upper semicontinuity in the properly defined functional space.\n

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