## Topological Methods in Nonlinear Analysis

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

Weiping Yan

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

#### Article information

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

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343903

Digital Object Identifier
doi:10.12775/TMNA.2015.055

Mathematical Reviews number (MathSciNet)
MR3443696

Zentralblatt MATH identifier
1362.76066

#### Citation

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. https://projecteuclid.org/euclid.tmna/1459343903

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