On the evolution of regularized Dirac-harmonic Maps from closed surfaces

TL;DR

This paper investigates the evolution of regularized Dirac-harmonic maps from closed surfaces, proving global existence of weak solutions, analyzing singularities, and exploring the possibility of removing regularization.

Contribution

It establishes the existence of global weak solutions for regularized Dirac-harmonic maps and discusses convergence and regularization removal.

Findings

Global weak solutions exist for the regularized problem.

Solutions are smooth except at finitely many singularities.

Convergence of the evolution equations is analyzed.

Abstract

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.