Global Well-Posedness of Landau–Lifshitz Flow With External Electromagnetic Field for Small Data in Three Dimensions

The Landau–Lifshitz–Maxwell system is an important model in magnetic storage devices, where the magnetization is affected by external electromagnetic fields. In this article, we are interested in the special case of the coupled system, that is, Gilbert damping parameter (Formula presented.) and magnetic permeability (Formula presented.), then we prove the global well-posedness for small data. After choosing the Coulomb gauge to rewrite the system, we perform energy estimate and Strichartz estimate to prove the global solution. Moreover, we obtain the scattering for the system under the Coulomb gauge.