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

## TL;DR

This paper proves the short time existence of the heat flow for Dirac-harmonic maps on closed Riemannian spin manifolds, extending previous results from manifolds with boundary.

## Contribution

It establishes the short time existence of the heat flow for Dirac-harmonic maps specifically on closed manifolds, filling a gap in the existing theory.

## Key findings

- Short time existence on closed manifolds proven.
- Extends previous results from manifolds with boundary.
- Provides a foundation for further analysis of Dirac-harmonic map flows.

## Abstract

The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of the classical heat flow for harmonic maps by coupling it to a spinor. It was 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.