Global Attractors of Evolutionary Systems
By A. Cheskidov. 2006
77 citations recorded by the source corpus.
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 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.
Subfields: Computer Networks and Communications, Control and Systems Engineering, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/df229d3a1d21050651d2aa9c2aa518227c4020fa
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In Computer Networks and Communications
In Control and Systems Engineering
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Citations in the corpus
- Blow-up in finite time for the dyadic model of the Navier-Stokes equations (2006, background): “ and finite time blow-up. Lastly, in Section 6 we discuss a weak global attractor for the dyadic model. The weak global attractor is the minimal weakly closed weakly attracting set. Using results from [3, 4], we show that the weak global attractor is also the maximal bounded invariant set. Moreover,f”
- Energy equality for the 3D critical convective Brinkman–Forchheimer equations (2016, methodology): “A similar result was given in the paper of Cheskidov et al. [4] where the energy equality was proved to hold for weak solutions of the NSE in the functional space L3(0, T ;D(A5/12)).”