Partial regularity to the Landau-Lifshitz equation with spin accumulation

Abstract

In this paper, we consider a model for the spin-magnetization system that takes into account the diffusion process of the spin accumulation. This model consists of the Landau-Lifshitz equation describing the precession of the magnetization, coupled with a quasi-linear parabolic equation describing the diffusion of the spin accumulation. This paper establishes the global existence and uniqueness of weak solutions for large initial data in R2. Moreover, partial regularity is shown. In particular, the solution is regular on R2×(0,∞) with the exception of at most finite singular points.