Partial regularity to the Landau-Lifshitz equation with spin accumulation

2018/08/06 by Xueke Pu, Pu, Xueke, Wendong Wang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1808.01798

openalex publication_date 2018/08/06 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

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 \Bbb R². Moreover, partial regularity is shown. In particular, the solution is regular on \Bbb R²×(0,∞) with the exception of at most finite singular points.

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