In this paper, we consider the global existence of one-dimensional nonautonomous inhomogeneous Schrödinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the one-dimensional nonautonomous inhomogeneous Schrödinger flow from S1 into a complete Kähler manifold with constant holomorphic sectional curvature admits a unique global smooth solution. As a corollary, we establish the global existence for the Cauchy problem of the inhomogeneous Heisenberg spin system.
On the Cauchy problem for the one-dimensional heat equation
