  We study a porous medium equation with fractional potential pressure: $$
\partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u, $$ for
$m>1$, $0<s<1$ and $u(x,t)\ge 0$. The problem is posed for $x\in \mathbb{R}^N$,
$N\geq 1$, and $t>0$. The initial data $u(x,0)$ is assumed to be a bounded
function with compact support or fast decay at infinity. We establish existence
of a class of weak solutions for which we determine whether the property of
compact support is conserved in time depending on the parameter $m$, starting
from the result of finite propagation known for $m=2$. We find that when $m\in
[1,2)$ the problem has infinite speed of propagation, while for $m\in [2,3)$ it
has finite speed of propagation. In other words $m=2$ is critical exponent
regarding propagation.
