Higher-order estimates of long-time solutions to the Kähler-Ricci flow

In this article, we study the higher-order regularity of Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates cylinders, proved that when generic fibers Iitaka fibration are biholomorphic to each other, converges in C loc ? -topology away from singular a negative Kähler-Einstein metric base manifold. particular, Ricci curvature is uniformly bounded any subsets other.