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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Smoothing and finite-dimensionality of uniform attractors in Banach spaces

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Author(s):
Cui, Hongyong [1] ; Carvalho, Alexandre N. [2] ; Cunha, Arthur C. [2] ; Langa, Jose A. [3]
Total Authors: 4
Affiliation:
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074 - Peoples R China
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[3] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo De Correos 1160, E-41080 Seville - Spain
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 285, p. 383-428, JUN 5 2021.
Web of Science Citations: 0
Abstract

The aim of this paper is to find an upper bound for the fractal dimension of uniform attractors in Banach spaces. The main technique we employ is essentially based on a compact embedding of some auxiliary Banach space into the phase space and a corresponding smoothing effect between these spaces. Our bounds on the fractal dimension of uniform attractors are given in terms of the dimension of the symbol space and the Kolmogorov entropy number of the embedding. In addition, a dynamical analysis on the symbol space is also given, showing that the finite-dimensionality of the hull of a time-dependent function is fully determined by the tails of the function, which allows us to consider more general non-autonomous terms than quasi-periodic functions. As applications, we show that the uniform attractor of the 2D Navier-Stokes equation is finite-dimensional in Hand in V, and that of a reaction-diffusion equation is finite-dimensional in L-2 and in L-p, with p > 2. (C) 2021 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 18/10997-6 - Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability
Grantee:Alexandre Nolasco de Carvalho
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 18/10634-0 - Estimates of the fractal dimension of attractors for autonomous and non-autonomous dynamical systems: applications
Grantee:Arthur Cavalcante Cunha
Support Opportunities: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 16/26289-5 - Estimates of the Fractal Dimension of Attractors for Autonomous and Non-Autonomous Dynamical Systems
Grantee:Arthur Cavalcante Cunha
Support Opportunities: Scholarships in Brazil - Doctorate