The Yamabe flow

Question

For a conformal class of metrics $\phi(t).g$, with $g$ a fixed metric, Yamabe define a Ricci flow:

$$\frac{\partial \phi}{\partial t}=\mu \Delta (\phi ) + \mu'  r(\phi.g)$$

with $r$, the scalar curvature, i.e. the trace of the Ricci curvature.

Have we solutions for the Yamabe flow?