The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

摘要

The Rosensweig instability is the phenomenon that above a certain thresholdof a vertical magnetic field peaks appear on the free surface of a horizontallayer of magnetic fluid. In contrast to almost all classical hydrodynamicalsystems, the nonlinearities of the Rosensweig instability are entirelytriggered by the properties of a deformed and a priori unknown surface. Theresulting problems in defining an adjoint operator for such nonlinearities areillustrated. The implications concerning amplitude equations for patternforming systems with a deformed surface are discussed.