Abstract: We consider a model which describes the 2D flow of a
conducting fluid surrounded by a ferromagnetic material, under the
influence of the hysteretic response of the surrounding medium. We
assume that this influence can be represented by the Preisach
operator. After a short introduction concerning hysteresis and
hysteresis operators, we will present the derivation of the model
problem and the existence and uniqueness results which hold in the
convexity domain of the Preisach operator. We will conclude with some
open problems.