Abstract

For the parabolic-elliptic Keller-Segel system in R-2 it has been proved that if the initial mass is less than 8 pi/chi, a global solution exists, and in case the initial mass is larger than 8 pi/chi, blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single species system? We find a threshold curve in the two species case that allows us to determine if the system is a blow-up or a global in time solution. No radial symmetry is assumed.