Conical Kähler-Ricci flows on Fano manifolds

In this paper, we study the long-term behavior of conical Kähler-Ricci flows on Fano manifolds. First, by proving uniform regularities for twisted Kähler-Ricci flows, we prove the existence of conical Kähler-Ricci flows by limiting these twisted flows. Second, we obtain uniform Perelman's estimates along twisted Kähler-Ricci flows by improving the original proof. After that, we prove that if there exists a conical Kähler-Einstein metric, then conical Kähler-Ricci flow must converge to it.