In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the "Riemann curvature" for the Ricci-harmonic flow generalizing a recently result of Simon \cite{Simon2015}.
Long time existence of the (n-1)-plurisubharmonic flow
Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature --- Part II
Long time existence of Minimizing Movement solutions of Calabi flow
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