  Let $(M^{n},g_{0})$ be a $n=3,4,5$ dimensional, closed Riemannian manifold of
positive Yamabe invariant. For a smooth function $K>0$ on $M$ we consider a
scalar curvature flow, that tends to prescribe $K$ as the scalar curvature of a
metric $g$ conformal to $g_{0}$. We show global existence and in case $M$ is
not conformally equivalent to the standard sphere smooth flow convergence and
solubility of the prescribed scalar curvature problem under suitable conditions
on $K$.
