Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations
DOI:
https://doi.org/10.12775/TMNA.2015.055Keywords
Magneto-hydrodynamics equations, periodic solution, Hopf bifurcation, stabilityAbstract
This paper is devoted to the study of the dynamical behavior for the 3D viscous Magneto-hydrodynamics equations. We first prove that this system under smooth external forces possesses time dependent periodic solutions, bifurcating from a steady solution. If the time periodic solution is smooth, then the linear stability of the time periodic solution implies nonlinear stability is obtained in $\textbf{L}^p$ for all $p\in(3,\infty)$.Downloads
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2015-09-01
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1.
YAN, Weiping. Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 471 - 493. [Accessed 24 April 2024]. DOI 10.12775/TMNA.2015.055.
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