Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces (Q493204)

The paper under review is concerned with the global well-posedness of the Landau-Lifshitz-Gilbert equation in the whole space for any initial data whose gradient belongs to the scaling-critical Morrey space. The proofs combine a priori estimates for solutions of a dissipative Schrödinger equation of Ginzburg-Landau type obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique.