The Chern-Kaehler flow

Question

Let $(M,\omega)$ be a Kaehler manifold, the Chern-Kaehler flow is defined by:

$$\frac{\partial \omega}{\partial t}= tr(R(\nabla^C))$$

where $R(\nabla^C)$ is the curvature of the Chern connection $\nabla^C$.

Have we solutions for short time of the Chern-Kaehler flow?