The Aronson-Benilan inequality, well known for the porous media equation $\partial_t \rho - \Delta \rho^m = 0$ provides a lower bound on the Laplacian of pressure: $\Delta \rho^{m-1} \geq C$. In this presentation, I will show that this estimate remains valid for another equation: the Keller-Segel system, which is a porous medium equation to which we add an aggregation term. Among other things, this provides a new demonstration of global existence for this system. I will focus on the case in dimension 2, with a linear diffusion and with a small initial mass but the result can be extended for any dimension, with the critical diffusion exponent and up to and including the critical mass. This work is in collaboration with Alejandro Jimenez-Fernandez (Oxford) and Filippo Santambrogio (Lyon).