Abstract

About 12 years ago the speaker and his colleague Wang Youde published a paper which proposed the notion of Schrodinger Flows inspired by the well-known Heisenberg model. This is an infinite dimensional Hamiltonnian system for maps from Riemannian manifolds into Kahler manifolds. In the past 10 years many research works have been done for Schrodinger Flows. In this lecture we will review some main results in the study of Schrodinger Flows, including local and global existence of the Cauchy problems, possible blow-up phenomenon, existence of self-similar solutions, time-periodic solutions and other special solutions.