In this talk,we describe an alternative approach to some quantitative results of Escobar and Schoen for metrics of prescribed scalar curvature on closed Riemannian manifolds with vanishing Yamabe invariant via a negative gradient curvature flow.The main result is to remove the so-called flatness condition proposed by Escobar and Schoen; hence answering a conjecture by Kadzan and Warner affirmatively.This talk is based on my joint work with Ngo Quoc Anh