A finite number of point observations which determine a non-autonomous fluid flow

Nonlinearity

Volumn 14, Issue 4, 2001, Pages 673-682

  Langa, José A ^a   Robinson, James C ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035402764     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/4/301     Document Type: Article

References (33)

1. Arnold L 1998 Random Dynamical Systems (Berlin: Springer)
2. Chepyzhov V and Vishik M 1993 A Hausdorff dimension estimate for kernel sections of non-autonomous evolution equations Indiana Univ. Math. J. 42 1057-76
3. -1994 Attractors of non-autonomous dynamical systems and their dimension J. Math. Pure. Appl. 73 279-333
4. Chueshov I D 2000 Gevrey regularity of random attractors for stochastic reaction-diffusion equations Random Operators Stock. Eq. 8 143-62
5. Cockburn B, Jones D A and Titi E S 1997 Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems Math. Comput. 66 1073-87
6. Constantin P and Foias C 1985 Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractor for 2D Navier-Stokes equation Commun. Pure Appl. Math. 38 1-27
7. -1988 Navier-Stokes Equations (Chicago, IL: University of Chicago Press)
8. Crauel H, Debussche A and Flandoli F 1995 Random attractors J. Dynam. Diff. Eq. 9 307-41
9. Crauel H and Flandoli F 1994 Attractors for random dynamical systems Prob. Theor. Relat. Fields 100 365-93
10. Debussche A 1998 Hausdorff dimension of a random invariant set J. Math. Pure. Appl. 77 967-88
11. Doering C R and Gibbon J D 1995 Applied Analysis of the Navier-Stokes Equations (Cambridge: Cambridge University Press)
12. Eden A, Foias C, Nicolaenko B and Temam R 1994 Exponential Attractorsfor Dissipative Evolution Equations (New York: Wiley)
13. Falconer K 1990 Fractal Geometry (Chichester: Wiley)
14. Foias C and Prodi G 1967 Sur le comportement global des solutions non stationnaires des équations de Navier-Stokes en dimension 2 Rend. Sem. Mat. Univ. Padova 39 1-34
15. Foias C, Sell G R and Temam R 1988 Inertial manifolds for nonlinear evolution equations J. Diff. Eq. 73 309-53
16. Foias C and Temam R 1984 Determination of the solutions of the Navier-Stokes equations by a set of nodal values Math. Comput. 43 117-33
17. -1989 Gevrey class regularity for the solutions of the Navier-Stokes equations J. Funct. Anal. 87 359-69
18. Foias C and Olson E J 1996 Finite fractal dimensions and Hölder-Lipschitz parametrization Indiana Univ. Math. J. 45 603-16
19. Friz P K, Kukavica I and Robinson J C 2001 Nodal parametrisation of analytic attractors Discrete Continuous Dynam. Syst. 7 643-57
20. Friz P K and Robinson J C 2001 Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values Physica D 148 201-20
21. Hale J K 1988 Asymptotic Behaviour of Dissipative Systems (Mathematics Surveys and Monographs vol 25) (Providence, RI: American Mathematical Society)
22. Hunt B R and Kaloshin V Y 1999 Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces Nonlinearity 12 1263-75
23. Hunt B R, Sauer T and Yorke J A 1992 Prevalence: a translation-invariant almost every for infinite dimensional spaces Bull Am. Math. Soc. 27 217-38
24. -1993 Prevalence: an addendum Bull. Am. Math. Soc. 28 306-7
25. Kloeden P and Schmalfuß B 1997 Nonautonomous systems, cocycle attractors and variable time-step discretization Numer. Algorithms 14 141-52
26. Ladyzhenskaya O A 1991 Attractors for Semigroups and Evolution Equations (Cambridge: Cambridge University Press)
27. Mañé 1981 On the Dimension of the Compact Invariant Sets of Certain Nonlinear Maps (Springer Lecture Notes in Mathematics vol 898) (Berlin: Springer) pp 230-42
28. Robinson J C 1999 Global attractors: topology and finite-dimensional dynamics J. Dynam. Diff. Eq. 11 557-81
29. -2001a A rigorous treatment of experimental observations for the two-dimensional Navier-Stokes equations Proc. R. Soc. A 457 1007-20
30. -2001b Infinite-Dimensional Dynamical Systems (Cambridge: Cambridge University Press)
31. Schmalfuß B 1992 Backward cocycles and attractors of stochastic differential equations Int. Seminar on Applied Mathematics - Nonlinear Dynamics: Attractor Approximation and Global Behaviour ed V Reitman, T Redrich and N Kosch pp 185-92
32. -2000 Attractors for the non-autonomous dynamical systems Proc. Equadiff 99 (Berlin) ed B Fielder, K Gröger and J Sprekels (Singapore: World Scientific) pp 684-9
33. Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Berlin: Springer, Providence, RI: American Mathematical Society) vol 68 (1996 2nd edn)