Pullback attractors for asymptotically compact non-autonomous dynamical systems
First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the similar concept in the autonomous framework. Our definition is different from that of asymptotic compactness already used in the theory of random and non-autonomous dynamical sys...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2006 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23702 |
| Acesso em linha: | http://hdl.handle.net/11441/23702 https://doi.org/10.1016/j.na.2005.03.111 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Non-autonomous (pullback) attractors energy method pullback asymptotically compact non-autonomous dynamical systems cocycle Navier-Stokes unbounded domains |
| Resumo: | First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the similar concept in the autonomous framework. Our definition is different from that of asymptotic compactness already used in the theory of random and non-autonomous dynamical systems (as developed by H. Crauel, F. Flandoli, P. Kloeden, B. Schmalfuss, amongst others) which means the existence of a (random or time-dependent) family of compact attracting sets. Next, we prove a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. This attractor is minimal and, in most practical applications, it is unique. Finally, we illustrate the theory with a 2D Navier-Stokes model in an unbounded domain. |
|---|