Abstract
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 $p\in(3,\infty)$.
Citation
Weiping Yan. "Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations." Topol. Methods Nonlinear Anal. 46 (1) 471 - 493, 2015. https://doi.org/10.12775/TMNA.2015.055
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