Topological Methods in Nonlinear Analysis

Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations

Weiping Yan

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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 $p\in(3,\infty)$.

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Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 471-493.

First available in Project Euclid: 30 March 2016

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Yan, Weiping. Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 471--493. doi:10.12775/TMNA.2015.055.

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