A 2-forms flow

Question

 Let $(M,g,J)$ be a hermitian manifold with $2$-forms $\omega_t$. I define a $2$-forms flow:

$$\frac{\partial \omega}{\partial t}=J(d^* \omega) \wedge  d^* \omega $$

with $d^*=*\circ d \circ *$, the co-differential.

Have we solutions of the $2$-forms flow for short time?