Local well-posedness of the Schrödinger flow into $\mathbb{S}^2$ with natural boundary conditions

Abstract

In this paper, we develop a new approximation scheme to solve the local well-posedness problem for the Schrödinger flow into the standard unit 2-sphere $\mathbb{S}^2\subset\mathbb{R}^3$ (i.e., the Landau-Lifshitz equation) with natural boundary conditions.