We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many singularities. Moreover, we discuss the convergence of the evolution equations and address the question if we can remove the regularization in the end.

中文翻译：

---

关于正则化狄拉克调和图从闭合曲面的演化


我们研究来自封闭黎曼曲面的狄拉克调和映射的正则化版本的演化方程。我们建立了正则化问题的全局弱解的存在性，该解远离有限多个奇点。此外，我们讨论了演化方程的收敛性，并解决了最终是否可以去除正则化的问题。