The second Kaehler-Ricci flow

Question

Let $(M,\omega)$ be a Kaehler manifold with Kaehler form $\omega$ and Ricci form $\rho$. The second Kaehler-Ricci flow is defined by the formula:

$$\frac{\partial \omega}{\partial t}=(\partial^* \rho) \wedge (\bar \partial^* \rho)$$

Can we find solutions of the second Kaehler-Ricci flow for small times?

The second Kaehler-Einstein manifolds are Kaehler manifolds such that:

$$\lambda \omega =(\partial^* \rho)\wedge (\bar \partial^* \rho)$$

$\lambda$ is a scalar.