Local Schrödinger flow into Kähler manifolds

Abstract

In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space R m into acompact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.