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 ${\mathbb{R}}^2$. Moreover, partial regularity is shown. In particular, the solution is regular on ${\mathbb{R}}^2\times (0,\infty )$ with the exception of at most finite singular points.