  In this paper we consider the incompressible porous media equation in the
Sobolev spaces $H^s(\R^2), s > 2$. We prove that for $T > 0$ the time $T$
solution map $\rho_0 \mapsto \rho(T)$ is nowhere locally uniformly continuous.
On the other hand we show that the particle trajectories are analytic curves in
$\R^2$.
