Global existence of weak solutions for Landau-Lifshitz-Maxwell equations
Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng · Discrete and Continuous Dynamical Systems · 2007
In this paper we study the model that the usual Maxwell's equations are supplemented with a constitution relation in which the electric displacement equals a constant time the electric field plus an internal polarization variable and the magnetic displacement equals a constant time the magnetic field plus the microscopic magnetization. Using the Galerkin method and viscosity vanishing approach, we obtain the existence of the global weak solution for the Landau-Lifshitz-Maxwell equations. The main difficulties in this study are due to the loss of compactness in the system.