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...
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| Veröffentlicht in: | Nonlinear analysis 2006-02, Vol.64 (3), p.484-498 |
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| creator | Caraballo, T. Łukaszewicz, G. Real, J. |
| description | 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 Crauel, Flandoli, Kloeden, 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. |
| doi_str_mv | 10.1016/j.na.2005.03.111 |
| format | Article |
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Finally, we illustrate the theory with a 2D Navier–Stokes model in an unbounded domain.</description><subject>Cocycle</subject><subject>Energy method</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Navier–Stokes</subject><subject>Non-autonomous (pullback) attractors</subject><subject>Partial differential equations</subject><subject>Pullback asymptotically compact non-autonomous dynamical systems</subject><subject>Sciences and techniques of general use</subject><subject>Topology. Manifolds and cell complexes. 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| ispartof | Nonlinear analysis, 2006-02, Vol.64 (3), p.484-498 |
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| subjects | Cocycle Energy method Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Navier–Stokes Non-autonomous (pullback) attractors Partial differential equations Pullback asymptotically compact non-autonomous dynamical systems Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Unbounded domains |
| title | Pullback attractors for asymptotically compact non-autonomous dynamical systems |
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