43 research outputs found
Global attractors of evolutionary systems
An abstract framework for studying the asymptotic behavior of a dissipative
evolutionary system 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.Comment: 21 page