Global attractors of evolutionary systems
| dc.creator | Cheskidov, Alexey | |
| dc.date | 2006-09-13 | |
| dc.date.accessioned | 2026-07-07T07:24:47Z | |
| dc.date.available | 2026-07-07T07:24:47Z | |
| dc.description | An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes equations (NSE) for which the existence of a semigroup of solution operators is not known. Each evolutionary system possesses a global attractor in the weak topology, but does not necessarily in the strong topology. In this paper we study the structure of a global attractor for an abstract evolutionary system, focusing on omega-limits and attracting, invariant, and quasi-invariant sets. We obtain weak and strong uniform tracking properties of omega-limits and global attractors. In addition, we discuss a trajectory attractor for an evolutionary system and derive a condition under which the convergence to the trajectory attractor is strong. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609357 | |
| dc.identifier | http://arxiv.org/abs/math/0609357 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116498 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 37L05; 76D05 | |
| dc.title | Global attractors of evolutionary systems | |
| dc.type | text |