Short time existence of the heat flow for Dirac-harmonic maps on closed manifolds

The heat flowfor Dirac-harmonicmaps on Riemannian spin manifolds is a modification of the classical heat flowfor harmonicmaps by coupling it to a spinor. Itwas introduced by Chen, Jost, Sun, and Zhu as a tool to get a general existence program for Dirac-harmonic maps. For source manifolds with boundary they obtained short time existence, and the existence of a global weak solution was established by Jost, Liu, and Zhu. We prove short time existence of the heat flow for Dirac-harmonic maps on closed manifolds