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

DOI: http://dx.doi.org/10.12775/TMNA.2015.055

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

#### Keywords

Magneto-hydrodynamics equations; periodic solution; Hopf bifurcation; stability

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