Pullback attractors of nonautonomous dynamical systems

Discrete and Continuous Dynamical Systems

Volumn 16, Issue 3, 2006, Pages 587-614

  Wang, Yejuan ^a,b   Zhong, Chengkui ^a   Zhou, Shengfan ^b  

^a LANZHOU UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

2D Navier Stokes system; Nonautonomous dynamical system; Pullback attractor

Indexed keywords

EID: 33845752454     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.16.587     Document Type: Article

References (26)

1. Z. Artstein, Uniform asymptotic stability in limiting equations, J. Differ. Equations, 27 (1978), 172-181.
2. T. Caraballo, J.A. Langa, Attractors for differential equations with variable delay, J. Math. Anal. Applns., 260 (2001), 421-438.
3. T. Caraballo, J.A. Langa, On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems, Dyn. Contin. Discret. Impulsive Syst., 10 (2003), 491-513.
4. D.N. Cheban, J. Duan, Almost periodic solutions and global attractors of non-autonomous Navier-Stokes equations, J. Dyn. Differ. Equations, 16 (2004), 1-34.
5. D.N. Cheban, P.E. Kloeden, B. Schmalfuß, The relationship between pullback, forwards and global attractors of nonautonomous dynamical systems, Nonlinear Dyn. Syst. Theory, 2 (2002), 9-28.
6. D.N. Cheban, Upper semicontinuity of attractors of non-autonomous dynamical systems for small perturbations, Electron. J. Differ. Equations, 42 (2002), 1-21.
7. V.V. Chepyzhov, M.I. Vishik, "Attractors of Equations of Mathematical Physics", American Mathematical Society, Providence, RI, 2002.
8. V.V. Chepyzhov, M.I. Vishik, W.L. Wendland, On non-autonomous sine-gordon type equations with a simple global attractor and some averaging, Discret. Contin. Dyn. Syst., 12 (2005), 27-38.
9. J.K. Hale, "Asymptotic Behaviour of Dissipative Systems", American Mathematical Society, Providence, 1988.
10. M.M. Hapaev, "Averaging in Stability Theory", Nauka, Moscow (1986); English transl, Kluwer Dordrech, 1992.
11. A.A. Ilyin, Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides, Sbornik Mathematics, 187 (1996), 635-677.
12. D.S. Li, P.E. Kloden, On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions, J. Differ. Equations, submitted.
13. D.S. Li and X.X. Zhang, On the stability in GDSs and differential inclusions, J. Math. Anal. Appl., 274 (2002), 705-724.
14. D.S. Li and P.E. Kloeden, Robustness of asymptotic stability to small time delays, Discret. Contin. Dyn. Syst., submitted.
15. Q.F. Ma, S.H. Wang, C.K. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana Univ. Math. J., 51 (2002), 1541-1559.
16. G.R. Sell, Y.C. You, "Dynamics of Evolutionary Equations", Springer, New York, 2002.
17. R. Temam, "Infinite Dimensional Dynamical System in Mechanics and Physics", 2nd Edition, Springer, New York, 1997.
18. Y.J. Wang, D.S. Li, P.E. Kloeden, On the asymptotical behavior of nonautonomous dynamical systems, Non. Anal. TMA, 59 (2004), 35-53.
19. S.S. Lu, H.Q. Wu, C.K. Zhong, Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces, Discret. Contin. Dyn. Syst., 8 (2005), 585-597.
20. K. Deimling, "Nonlinear Functional Analysis", Springer, Berlin, 1985.
21. H. Brézis and T. Gallouet. Nonlinear Schrödinger evolution equation, Non. Anal., 4 (1980), 677.
22. C. Foias, O. Manley, R. Temam, Y. Treve, Asymptotic analysis of the Navier-Stokes equations, Physica D, 6 (1983), 157-188.
23. J. Robinson, "Infinite Dimensional Dynamical Systems", Cambridge University Press, 2001.
24. V.P. Bongolan-Walsh, D. N. Cheban, J. Duan, Recurrent motion in the nonautonomous Navier-Stokes system, Discret. Contin. Dyn. Syst. (B), 3 (2003), 255-262.
25. Yanren Hou, Kaitai Li, The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain, Non. Anal. TMA, 58 (2004), 609-630.
26. P.E. Kloeden and V.S. Kozyakin, The perturbation of attractors of skew-product flows with a shadowing driving system, Discret. Contin. Dyn. Syst., 7 (2001), 883-893.