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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.Comment: 11 pages, 1 figur

THE ADJOINT PROBLEM IN THE PRESENCE OF A DEFORMED SURFACE: THE EXAMPLE OF THE ROSENSWEIG INSTABILITY ON MAGNETIC FLUIDS