Convergence of the empirical measure for the Keller-Segel model in both subcritical and critical cases
Résumé
We show the weak convergence, up to extraction of a subsequence, of the empirical measure for the Keller-Segel system of particles in both subcritical and critical cases. We use a simple two particles moment argument in order to show that the particle system does not explodes in finite time, uniformly in the number of particles in some sense.