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In this note, we prove the existence of weak solutions of the Chern-Ricciflow through blow downs of exceptional curves, as well as backwards smoothconvergence away from the exceptional curves on compact complex surfaces. Thesmoothing property for the Chern-Ricci flow is also obtained on compactHermitian manifolds of dimension n under a mild assumption.

Weak Solutions of the Chern-Ricci flow on compact complex surfaces