Hopf-bifurcation theorem and stability for the magneto-hydrodynamics equations - Yan, Weiping (Topological Methods in Nonlinear Analysis, 2015)
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 L^p for all p(3,∞).