Energy methods in dissipative magnetohydrodynamics

A brief summary of energy methods for linear stability in dissipative magnetohydrodynamics is given. In this case, the methods are equally efficient for fixed and free boundary problems. Linear asymptotic stability has implications in nonlinear stability, at least for a modest but finite level of perturbations. Sufficient conditions for nonlinear stability of dissipative magneto-hydrodynamics flows are obtained and applied to the time dependent magnetized Couette flow. The fluid has a plate as boundary and nonlinear stability is unconditional. The range of stable Reynolds numbers is rather modest i.e. of the order of 2#pi#"2#approx#20. Nonlinear stability of force free fields can be treated very successfully for all values of dissipation and all levels of perturbations. It requires, however, the presence of perfectly conducting fixed boundaries. Finally, a special inertia-caused Hopf bifurcation is identified and illustrated by an appropriate example. (orig.)SIGLEAvailable from TIB Hannover: RA 71(6/321) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman