Some results on the Yang-Mills flow and its application

Min-Chun Hong (Queensland)

Abstract

At first, I will outline some old and new results on the Yang-Mills flow. Then we establish a parabolic gauge fixing theorem and used it to present a new proof of the existence of the weak solution of the Yang-Mills flow over a four dimensional manifold with initial value in $H^1$. Finally, we improve a key lemma of Uhlenbeck and prove the uniqueness of the weak solution of the Yang-Mills flow on a four dimensional manifold.