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...
| Authors: | , |
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| 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 |
| 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. |
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