The Lee flows

Question

Let $(M,g)$ be a riemannian manifold. I define two Lee flows, $\theta$ is a 1-form and $\omega$ is a 2-form.

$$\frac{\partial \theta}{\partial t}= \iota (\theta^*)(d\theta)$$

$$\frac{\partial \omega}{\partial t}= \iota ( (d^* w)^*)(d\omega)$$

with $\iota (X)(\omega)(Y_i)=\omega (X,Y_i)$.

Have we solutions for the Lee flows?