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.
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