Journal
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume 21, Issue 2, Pages 249-268Publisher
SPRINGER
DOI: 10.1007/s10884-009-9133-x
Keywords
Evolutionary system; Global attractor; Navier-Stokes equations
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Funding
- NSF DMS [0807827]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0943680] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0807827] Funding Source: National Science Foundation
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An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system E with respect to weak and strong topologies was introduced in Cheskidov and Foias (J Differ Equ 231: 714-754, 2006) 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.
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