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.

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.