Federico Buseghin (Cergy)

Finite time blow-up for the Keller-Segel system.

The Keller-Segel system is a model for chemotactic aggregation and is a nonlocal non-linear reaction diffusion equation. I will discuss existence of solutions with type II finite time blow-up in the 3-dimensional, axially-symmetric case. An intermediate step is a construction by gluing techniques of finite time blow-up solutions in the 2-dimensional case. This is a joint work with Juan Dávila, Manuel del Pino and Monica Musso.