Partial regular solution to the Landau–Lifshitz–Maxwell system with spin accumulation in two dimensions

Abstract

We establish the existence, uniqueness, and singularities of coupled spin polarized transport equations in two dimensions. This coupled system includes Landau–Lifshitz–Maxwell equation, and a quasilinear parabolic equation describing the diffusion of spin accumulation. The approach bases on the Leray–Schauder fixed point theory and Moser iterative method; we prove strictly that there exists a weak regular solution except at most finite singular points.