  The goal of this paper is to exhibit a critical mass phenomenon occuring in a
model for cell self-organization via chemotaxis. The very well known dichotomy
arising in the behavior of the macroscopic Keller-Segel system is derived at
the kinetic level, being closer to microscopic features. Indeed, under the
assumption of spherical symmetry, we prove that solutions with initial data of
large mass blow-up in finite time, whereas solutions with initial data of small
mass do not. Blow-up is the consequence of a virial identity and the existence
part is derived from a comparison argument. Spherical symmetry is crucial
within the two approaches. We also briefly investigate the drift-diffusion
limit of such a kinetic model. We recover partially at the limit the
Keller-Segel criterion for blow-up, thus arguing in favour of a global link
between the two models.

Analysis of PDEs