Schrödinger Flows on Compact Hermitian Symmetric Spaces and Related Problems

Abstract

In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions to the initial value problem of Heisenberg model wit Lie algebra values, which is closely related to the Schrodinger flow on compact Hermitian symmetric spaces.