Magnetohydrodynamic flow with hysteresis

We consider a model system describing the two-dimensional \ufb02ow of a conducting \ufb02uid surrounded by a ferromagnetic solid under the in\ufb02uence of the hysteretic response of the surrounding medium. We assume that this in\ufb02uence can be represented by the Preisach hysteresis operator. Existence and uniqueness of solutions for the resulting system of PDEs with hysteresis nonlinearities is established in the convexity domain of the Preisach operator