Weak and strong solutions to Landau-Lifshitz-Bloch-Maxwell equations with polarization

Abstract The Landau-Lifshitz-Bloch-Maxwell equations with polarization describe the evolution of the mean fields in continuous ferromagnetics. In this paper, we firstly use the energy method to prove the existence of weak solution to the Landau-Lifshitz-Bloch-Maxwell equations with polarization for the viscosity problem in two dimensions. Then we prove that the estimates are uniformed in ϵ for solutions to viscosity problem, and letting ϵ → 0 we obtain the global weak solution for the Landau-Lifshitz-Bloch-Maxwell equations with polarization. Finally combining the a p r i o r i estimates, we obtain the existence of smooth solutions for the Landau-Lifshitz-Bloch-Maxwell equations with polarization in two dimensions.