The positiv Ricci flow

Question

Let $(M,g_t)$ be a riemannian manifold, I define the positiv Ricci flow:

$$\frac{\partial g}{\partial t}=-2|Ric|(g)$$ 

where $Ric$ is the Ricci curvature and $|Ric|=\sqrt{(Ric)^2}$, it is the absolute value of the associated symmetric endomorphism of the tangent bundle. We could also take $Ric^2$ instead of $|Ric|$.

Is the positiv Ricci flow well-defined? Have we singularities for the flow?