Chepyzhov, V. V.; Ilyin, A. A. A note on the fractal dimension of attractors of dissipative dynamical systems. (English) Zbl 1153.37438 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 811-819 (2001). Cited in 21 Documents MSC: 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35B41 Attractors 47H20 Semigroups of nonlinear operators Keywords:Fractal dimension; attractors; Navier-Stokes equations; applications to evolution equations; reaction-diffusion system PDFBibTeX XMLCite \textit{V. V. Chepyzhov} and \textit{A. A. Ilyin}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 811--819 (2001; Zbl 1153.37438) Full Text: DOI References: [1] A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, Nauka, Moscow, 1989 (English transl., North-Holland, Amsterdam, 1992).; A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, Nauka, Moscow, 1989 (English transl., North-Holland, Amsterdam, 1992). · Zbl 0804.58003 [2] Chen, Z., A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors, Chaos Solitons Fractals, 3, 575-582 (1993) · Zbl 0783.58044 [3] Douady, A.; Oesterlé, J., Dimension de Hausdorff des attracteurs, C.R. Acad. Sci. Paris, Sér. A, 290, 1135-1138 (1980) · Zbl 0443.58016 [4] Ilyin, A. A., Attractors for Navier-Stokes equations in domains with finite measure, Nonlinear Anal. Theory Methods Appl., 27, 605-616 (1996) · Zbl 0859.35090 [5] Ladyzhenskaya, O. A., First boundary value problem for Navier-Stokes equations in domain with non smooth boundaries, C.R. Acad. Sci. Paris, 314, 253-258 (1992) · Zbl 0744.35034 [6] Li, P.; Yau, S. T., On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys., 8, 309-318 (1983) · Zbl 0554.35029 [7] Sh.M. Nasibov, On optimal constants in some Sobolev inequalities and their applications to a nonlinear Schrödinger equation, Dokl. Akad. Nauk SSSR 307 (1989) 538-542 (English transl., Soviet Math. Dokl. 40 (1990) 110-115).; Sh.M. Nasibov, On optimal constants in some Sobolev inequalities and their applications to a nonlinear Schrödinger equation, Dokl. Akad. Nauk SSSR 307 (1989) 538-542 (English transl., Soviet Math. Dokl. 40 (1990) 110-115). [8] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd Edition, Springer, New York, 1997.; R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd Edition, Springer, New York, 1997. · Zbl 0871.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.