The partial regularity for Landau-Lifshitz-Maxwell-Spin diffusion system in three dimensions

Abstract

In this paper, we consider the model of the Landau-Lifshitz-Maxwell system coupled with spin accumulation. This system consists of the Landau-Lifshitz equation, Maxwell equation describing the magnetic field and a quasi-linear parabolic equation describing the process of spin accumulation. This paper establishes the existence of weak solutions (M,S,H,E) to the coupled system in three dimensions and shows the magnetization vector field M is Hölder continuous except a closed set Σ, which has locally finite 3-dimensional parabolic Hausdorff measure. Finally, we deduce the Hölder continuity of ∇M away from Σ in two special cases.