The LCK-Ricci flow

Question

For a LCK metric $\omega$:

$$d\omega +\theta \wedge \omega=0$$

$$d\theta =0$$

we can define the LCK-Ricci flow:

$$ \frac{\partial \omega}{\partial t}=\rho$$

where $\rho$ is the Ricci curvature.

Have we solutions for the  LCK-Ricci flow? What are the conditions for having such a flow?