$C^{2,\alpha }$-estimate for conical K\"ahler-Ricci flow

We establish a parabolic version of Tian’s $C^{2,\alpha }$-estimate for conical complex Monge-Ampere equations, which includes conical K"ahler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical K"ahler-Ricci flow in arXiv:1411.7284.