The Landau-Lifshitz equation of the ferromagnetic spin chain and Oseen-Frank flow

Abstract

In this paper, we consider the Landau-Lifshitz equation of the ferromagnetic spin chain from ${\mathbb{R}}^2$ to the unit sphere $S^2$ under the general Oseen-Frank energy. We obtain global existence and uniqueness of weak solutions for large energy data; moreover, the number of singular points is finite.