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We show that the scalar curvature is uniformly bounded for the normalized K\"ahler-Ricci flow on a K\"ahler manifold with semi-ample canonical bundle. In particular, the normalized K\"ahler-Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for K\"ahler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.

Bounding scalar curvature for global solutions of the Kähler-Ricci flow