LOCAL CAUCHY PROBLEM FOR YANG-MILLS HEAT FLOWS

Abstract

In this paper, we are interested in the following nonlinear heat equation

,

studied by Grotowski in 2001 in studying the special solutions for s Yang-Mills heat flows. We aim to study the Cauchy problem for the equation. We reply on the regularity of the semi-group  Firstly, the model is not compatible with the semi-group, we need to transfer to another one and the main difficulty is to handle the unbounded nonlinearity  Finally, we proved the Cauchy problem for the model that for any initial data , there exists  such that the above equation has a unique solution  for all .