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 IJMNTA  Vol.4 No.3 , September 2015
Inertial Manifolds for 2D Generalized MHD System
Abstract: In this paper, we prove the existence of inertial manifolds for 2D generalized MHD system under the spectral gap condition.
Cite this paper: Yuan, Z. , Guo, L. and Lin, G. (2015) Inertial Manifolds for 2D Generalized MHD System. International Journal of Modern Nonlinear Theory and Application, 4, 190-203. doi: 10.4236/ijmnta.2015.43014.
References

[1]   Yuan, Z.Q., Guo, L. and Lin, G.G. (2015) Global Attractors and Dimension Estimation of the 2D Generalized MHD System with Extra Force. Applied Mathematics, 6, 724-736.
http://dx.doi.org/10.4236/am.2015.64068

[2]   Lin, G.G. (2009) An Inertial Manifold of the 2D Swift-Hohenberg Equation. Journal of Yunnan University, 31, 334-340.

[3]   Temam, R. (1988) Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer, New York.
http://dx.doi.org/10.1007/978-1-4684-0313-8

[4]   Constantin, P., Foias, C., Nicolaenko, B. and Temam, R. (1989) Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-3506-4

[5]   Lin, G.G. (2011) Nonlinear Evolution Equations. Yunnan University, Kunming.

[6]   Babin, A.V. and Vishik, M.I. (1992) Attractors of Evolution Equations. North-Holland, Amsterdam.

[7]   Chow, S.-N. and Lu, K. (1988) Invariant Manifolds for Flows in Banach Spaces. Journal of Differential Equations, 74, 285-317.
http://dx.doi.org/10.1016/0022-0396(88)90007-1

[8]   Chueshov, I.D. (1992) Introduction to the Theory of Inertial Manifolds, (Lecture Notes). Kharkov Univ. Press, Kharkov (in Russian).

[9]   Chueshov, I.D. (1999) Introduction to the Theory of Infinite-Dimensional Dissipative Systems. Acta, Kharkov (in Russian) (English Translation, 2002, Acta, Kharkov).

[10]   Henry, D. (1981) Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840. Springer, Berlin-Heidelberg and New York.

[11]   Leung, A.W. (1989) Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering. MIA, Kluwer, Boston.

 
 
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