Global lyapunov exponents, kaplan‐yorke formulas and the dimension of the attractors for 2D navier‐stokes equations

Communications on Pure and Applied MathematicsVolume 38, Issue 1 p. 1-27 Article Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations P. Constantin, P. Constantin Indiana UniversitySearch for more papers by this authorC. Foias, C. Foias Indiana UniversitySearch for more papers by this author P. Constantin, P. Constantin Indiana UniversitySearch for more papers by this authorC. Foias, C. Foias Indiana UniversitySearch for more papers by this author First published: January 1985 https://doi.org/10.1002/cpa.3160380102Citations: 155AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 Babin, A. V., and Vishik, M. I., Attractors of quasilinear parabolic equations, Dokladi Akad. Nauk S. S. S. R. 264, 1982, pp. 780–784. (in Russian.) 2 Babin, A. V., and Vishik, M. I., Existence and estimate of the dimension of the attractors of quasilinear parabolic equations and Navier-Stokes systems, Uspehi Mat. Nauk 3, 1982, p. 225. (in Russian.) 3 Constantin, P., and Foias, C., Sur le transport des variétes de dimension finite par les solutions des équations de Navier-Stokes, C. R. Acad. Sci. Paris, t. 296, série I, 10 Janvier 1983, pp. 23–26. 4 Douady, A., and Oesterlé, J., Dimension de Hausdorff des attracteurs, C. R. Acad. Sci. Paris, t. 290, série A, 30 Juin 1980, pp. 1135–1138. 5 Farmer, D., Chaotic attractors of an infinite dimensional system, Physica D 4D, 1982, pp. 366–393. 6 Foias, C., Solutions statistiques des équations de Navier-Stokes, Cours au College de France, 1974, mimeographed notes. 7 Foias, C., Guillopé, C., and Temam, R., New apriori estimates for Navier-Stokes equations in dimension 3, Comm. in P. D. E. 6, 1981, pp. 329–359 8 Foias, C., Manley, O., Temam, R., and Trève, Y., Asymptotic analysis of the Navier-Stokes equations, Physica D., 1983, pp. 157–188. 9 Foias, C., and Prodi, G., Sur le comportement global des solutions nonstationnaires des équations de Navier-Stokes en dimension 2, Rend. Sem. Padova 39, 1967, pp. 1–34. 10 Foias, C., and Temam, R., Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures et Appl. 58, 1979, pp. 339–368. 11 Foias, C., and Temam, R., On the Hausdorff dimension of an attractor for the two-Dimensional Navier-Stokes equations, Physics Letters 93A, 1983, pp. 451–454. 12 Hartman, P., Ordinary Differential Equations, Birkhäuser, Boston, 1982, p. 242. 13 Kaplan, J., and Yorke, J., Chaotic behaviour of multidimensional difference equations, Functional Differential Equations and Approximation of Fixed Points, H. O. Peitgen and H. O. Walther, editors, Lecture Notes in Mathematics 730, Springer, Berlin, 1979, p. 219. 14 Kato, T., Perturbation Theory for Linear Operators, Springer, Berlin, 1976. 15 Ladyzhenskaia, O. A., On the finite dimensionality of bounded invariant sets for dissipative problems, Dokladi Adad. Nauk S. S. S. R. 263, 1982, pp. 802–804. (in Russian.) 16 Mallet-Paret, J., Negatively invariant sets of compact maps and extension of a theorem by Cartwright, J. Diff. Eq. 22, 1976, pp. 331–248. 17 Mandelbrot, B., Fractals: Form, Chance and Dimension, Freeman, San Francisco, 1977. 18 Métivier, G., Valeurs propres d'opérateurs définis par la restriction de systèmes variationels à des sous espaces, J. Math. Pures et Appl. 57, 1978, pp. 133–156. 19 Minea, Gh., Remarques sur l'unicité de la solution stationnaire d'une équation de type Navier-Stokes, Revue Roumaine de Math. Pures et Appl. 21, 1976, pp. 1071–1075. 20 Ruelle, D., Ergotic theory of differential dynamical systems, Publications Mathematiques IHES 50, 1979, pp. 275–306. 21 Ruelle, D., Large volume limit of the distribution of charactertics exponents in turbulence, IHES preprint 82145. 22 Stein, E., Singular Integrals and the Differentiability Properties of Functions, Princeton University Press, 1970. 23 Temam, R., Navier-Stokes equations and nonlinear functional analysys, NSF/CBMS Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983. Citing Literature Volume38, Issue1January 1985Pages 1-27 ReferencesRelatedInformation