Perturbations of foliated bundles and evolutionary equations

Annali di Matematica Pura ed Applicata

Volumn 185, Issue SUPPL. 5, 2006, Pages

  Pliss, Victor A ^a   Sell, George R ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Evolutionary equations; Navier Stokes equations; Proper negative continuation; Quasiperiodic; Skew product dynamics

Indexed keywords

EID: 33748858723     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-004-0148-y     Document Type: Article

References (36)

1. Agmon, S., Nirenberg, L.: Properties of solutions of ordinary differential equations in Banach space. Commun. Pure Appl. Math. 16, 121-239 (1963)
2. Anosov, D.V.: Geodesic flows on closed Riemannian manifolds of negative curvature. Trudy Mat. Inst. Steklov 90, 209 (1967)
3. Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations. Berlin, Heidelberg, New York: Springer 1983
4. Bardos, C., Tartar, L.: Sur l'unicité rétrograde des équations paraboliques et quelques équations voisine. Arch. Ration. Mech. Anal. 50, 10-25 (1973)
5. Bates, P.W., Lu, K., Zeng, C.: Existence and persistence of invariant manifolds for semiflows in Banach spaces. Mem. Am. Math. Soc. 135 no. 645 (1998)
6. Besicovitch, A.S.: Almost Periodic Functions. New York: Dover 1932/1955
7. Cartwright, M.L.: Almost periodic flows and solutions of differential equations. Proc. Lond. Math. Soc. 17, 355-380 (1967)
8. Cartwright, M.L.: Almost periodic equations and almost periodic flows. J. Differ. Equations 5, 167-181 (1969)
9. Fenichel, N.: Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193-226 (1971)
10. Fink, A.M.: Almost Periodic Differential Equations. Lect. Notes Math., vol. 377. Berlin, Heidelberg, New York: Springer 1974
11. Hale, J.K.: Asymptotic Behavior of Dissipative Systems. Math Surveys and Monographs, vol. 25. Providence, RI: Am. Math. Soc. 1988
12. Henry, D.B.: Geometric Theory of Semilinear Parabolic Equations. Lect. Notes Math., vol. 840. Berlin, Heidelberg, New York: Springer 1981
13. Henry, D.B.: Some infinite dimensional Morse-Smale systems defined by parabolic partial differential equations. J. Differ. Equations 53, 401-458 (1985)
14. Hirsch, M.W., Pugh, C.C., Shub, M.: Invariant Manifolds. Lect. Notes Math., vol. 583. Berlin, Heidelberg, New York: Springer 1977
15. Kamaev, D. A.: Hyperbolic limit sets of evolutionary equations and the Galerkin method. Russ. Math. Surv. 35, 239-243 (1980)
16. Kelley, J.L., Namioka, I.: Linear Topological Spaces. Grad. Texts Math., no. 36. Berlin, Heidelberg, New York: Springer 1976
17. Lions, J.L., Malgrange, B.: Sur l'unicité rétrograde dans les problèmes mixtes paraboliques. Math. Scand. 8, 277-286 (1960)
18. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci., vol. 44. Berlin, Heidelberg, New York: Springer 1983
19. Pilyugin, S.Y.: Introduction to Structurally Stable Systems of Differential Equations. Russian version: Vvedenie v grubye sistemy differentsial'nykh uravneniy (1988). Boston: Birkhäuser 1992
20. Pliss, V.A., Sell, G.R.: Perturbations of attractors of differential equations. J. Differ. Equations 92, 100-124(1991)
21. Pliss, V.A., Sell. G.R.: Approximation dynamics and the stability of invariant sets. J. Differ. Equations 149, 1-51 (1998)
22. Pliss, V.A., Sell, G.R.: Robustness of exponential dichotomies in infinite dimensional dynamical systems. J. Dyn. Differ. Equations 11, 471-513 (1999)
23. Pliss. V.A., Sell, G.R.: On the stability of normally hyperbolic sets of smooth flows. Dokl. Akad. Nauk 378, 153-154 (2000)
24. Pliss, V.A., Sell, G.R.: Perturbations of normally hyperbolic manifolds with applications to the Navier-Stokes equations. J. Differ. Equations 169, 396-492 (2001)
25. Pugh. C., Shub, M., Starkov, A.: Stable ergodicity. Bull. Am. Math. Soc. 41, 1-41 (2004)
26. Raugel, G., Sell, G.R.: Navier-Stokes equations on thin 3D domains III: Global and local attractors. In: Sell, G.R., Foias, C., Temam, R. (eds.): Turbulence in Fluid Flows: A Dynamical Systems Approach. IMA Volumes in Mathematics and its Applications, vol. 55 pp. 137-163. Berlin, Heidelberg, New York: Springer 1993
27. Robinson, C., Young, L.-S.: Nonabsolutely continuous foliations for an Anosov diffeomorphism. Invent. Math. 61, 159-176 (1980)
28. Sacker, R.J.: A perturbation theorem for invariant manifolds and Holder continuity. J. Math. Mech. 18, 705-762 (1969)
29. Sacker, R.J., Sell, G.R.: Existence of dichotomies and invariant splittings for linear differential systems, I. J. Differ. Equations 15, 429-458 (1974)
30. Sacker, R.J., Sell, G.R.: Existence of dichotomies and invariant splittings for linear differential systems, II. J. Differ. Equations 22, 478-496 (1976)
31. Sacker, R.J., Sell, G.R.: Existence of dichotomies and invariant splittings for linear differential systems, III. J. Differ. Equations 22, 497-522 (1976)
32. Sell, G.R.: Nonautonomous differential equations and topological dynamics: I. The basic theory; and II. Limiting equations. Trans. Am. Math. Soc. 127, 241-262, 263-283 (1967)
33. Sell, G.R., You, Y.: Dynamics of Evolutionary Equations. Appl. Math. Sci., vol. 143. Berlin, Heidelberg, New York: Springer 2002
34. Shen, W., Yi, Y.: Almost automoiphic and almost periodic dynamics in skew product semiflows. Mem. Am. Math. Soc. 136, no. 647 (1998)
35. Smale, S.: Differentiable dynamical systems. Bull. Am. Math. Soc. 73, 747-817 (1967)
36. Temam, R.: Infinite Dimensional Dynamical Systems in Mechanics and Physics. Berlin, Heidelberg, New York: Springer 1988