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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 503454, 12 pages
The Exponential Attractors for the g-Navier-Stokes Equations
1College of Modern Science and Technology, China Jiliang University, Hangzhou 310018, China
2College of Science, China Jiliang University, Hangzhou 310018, China
Received 6 February 2012; Accepted 2 May 2012
Academic Editor: Pankaj Jain
Copyright © 2012 Delin Wu and Jicheng Tao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Roh, “Dynamics of the -Navier-Stokes equations,” Journal of Differential Equations, vol. 211, no. 2, pp. 452–484, 2005.
- J. Roh, g-Navier-stokes equations [thesis], University of Minnesota, 2001.
- O. A. Ladyzhenskaya, “On the dynamical system generated by the Navier-Stokes equations,” Zapiskii of Nauchnish Seminarovs LOMI, vol. 27, pp. 91–114, 1972, English translation: Journal of Soviet Mathematics, vol. 3, 1975.
- C. Foiaş and R. Temam, “Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations,” Journal de Mathématiques Pures et Appliquées, vol. 58, no. 3, pp. 339–368, 1979.
- J. Mallet-Paret, “Negatively invariant sets of compact maps and an extension of a theorem of Cartwright,” Journal of Differential Equations, vol. 22, no. 2, pp. 331–348, 1976.
- P. Constantin and C. Foias, Navier-Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill, USA, 1988.
- V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, vol. 49 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 2002.
- J. K. Hale, Asymptotic Behavior of Dissipative Systems, vol. 25 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1988.
- A. Haraux, Systèmes Dynamiques Dissipatifs et Applications, vol. 17 of Recherches en Mathématiques Appliquées, Masson, Paris, France, 1991.
- S. S. Lu, H. Q. Wu, and C. K. Zhong, “Attractors for non-autonomous 2D Navier-Stokes equations with normal external forces,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 8, pp. 585–597, 2005.
- Q. Ma, S. Wang, and C. Zhong, “Necessary and sufficient conditions for the existence of global attractors for semigroups and applications,” Indiana University Mathematics Journal, vol. 51, no. 6, pp. 1541–1559, 2002.
- R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol. 68 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2nd edition, 1997.
- D. Wu, “On the dimension of the pullback attractors for -Navier-Stokes equations,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 893240, 16 pages, 2010.
- D. Wu and C. Zhong, “The attractors for the nonhomogeneous nonautonomous Navier-Stokes equations,” Journal of Mathematical Analysis and Applications, vol. 321, no. 1, pp. 426–444, 2006.
- A. Eden, C. Foias, B. Nicolaenko, and R. Temam, Exponential Attractors for Dissipative Evolution Equations, vol. 37 of Research in Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1994.
- M. Efendiev, S. Zelik, and A. Miranville, “Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems,” Proceedings of the Royal Society of Edinburgh. Section A, vol. 135, no. 4, pp. 703–730, 2005.
- A. Miranville and S. V. Zelik, “Attractors for dissipative partial differential equations in bounded and unbounded domains,” in Handbook of Differential Equations, Evolutionary Equations, C. M. Dafermos and M. Pokorny, Eds., vol. 4, Elsevier, Amsterdam, The Netherlands, 2008.
- M. Efendiev and A. Yagi, “Continuous dependence on a parameter of exponential attractors for chemotaxis-growth system,” Journal of the Mathematical Society of Japan, vol. 57, no. 1, pp. 167–181, 2005.
- M. Efendiev, A. Miranville, and S. Zelik, “Exponential attractors for a nonlinear reaction-diffusion system in ,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 330, no. 8, pp. 713–718, 2000.
- L. Dung and B. Nicolaenko, “Exponential attractors in Banach spaces,” Journal of Dynamics and Differential Equations, vol. 13, no. 4, pp. 791–806, 2001.
- A. Babin and B. Nicolaenko, “Exponential attractors of reaction-diffusion systems in an unbounded domain,” Journal of Dynamics and Differential Equations, vol. 7, no. 4, pp. 567–590, 1995.
- A. Eden, C. Foias, and V. Kalantarov, “A remark on two constructions of exponential attractors for -contractions,” Journal of Dynamics and Differential Equations, vol. 10, no. 1, pp. 37–45, 1998.
- M. Efendiev, A. Miranville, and S. Zelik, “Exponential attractors for a singularly perturbed Cahn-Hilliard system,” Mathematische Nachrichten, vol. 272, pp. 11–31, 2004.
- M. Efendiev, A. Miranville, and S. Zelik, “Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system,” Mathematische Nachrichten, vol. 248/249, pp. 72–96, 2003.
- Y. Zhong and C. Zhong, “Exponential attractors for reaction-diffusion equations with arbitrary polynomial growth,” Nonlinear Analysis, vol. 71, no. 3-4, pp. 751–765, 2009.
- M. Kwak, H. Kwean, and J. Roh, “The dimension of attractor of the 2D -Navier-Stokes equations,” Journal of Mathematical Analysis and Applications, vol. 315, no. 2, pp. 436–461, 2006.