摘要：The Hermitian-Yang-Mills flow was first introduced by Donaldson. When the base manifold is a compact K\"ahler manifold, this flow coincides with the Yang-Mills flow. In this talk, we introduce our recent results on the long-time behavior of the Hermitian-Yang-Mills flow over non-K\"ahler manifolds. As its applications, we establish a sharp generalized Bogomolov inequality on holomorphic vector bundle, furthermore we characterize the equality case. These works are joint with Zeng Chen, Chao Li and Chuanjing Zhang.