Current-induced magnetization dynamics. Global existence of weak solutions

We consider a model of current-induced magnetization dynamics described by the Landau–Lifshitz–Gilbert (LLG) equations of the magnetization, in which an additional current dependent term is added. Two methods, namely Faedo–Galerkin/Penalty (FGP) method and hyperbolic regularization method are used to show the existence of finite energy global weak solutions.