On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems

For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefu...

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Bibliographic Details
Authors: Marín Rubio, Pedro, Real Anguas, José
Format: article
Status:Versión aceptada para publicación
Publication Date:2009
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25936
Online Access:http://hdl.handle.net/11441/25936
https://doi.org/10.1016/j.na.2009.02.065
Access Level:Open access
Keyword:Pullback attractors
Non-autonomous dynamical systems
Tempered sets
Description
Summary:For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier–Stokes model, improving some previous results on attractor theory.