  In this work, we obtain some existence results of Chern-Ricci Flows and the
corresponding Potential Flows on complex manifolds with possibly incomplete
initial data. We discuss the behaviour of the solution as $t\rightarrow 0$.
These results can be viewed as generalization of an existence result by Giesen
and Topping for surfaces of hyperbolic type of Ricci flow to higher dimensions
in certain sense. On the other hand, we also discuss the long time behaviour of
the solution and obtain some sufficient conditions for the existence of
K\"ahler-Einstein metric on complete noncompact Hermitian manifolds, which
generalizes the work of Lott-Zhang and Tosatti-Weinkove to complete noncompact
Hermitian manifolds with possibly unbounded curvature.
