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The goal of this paper is to exhibit a critical mass phenomenon occuring in amodel for cell self-organization via chemotaxis. The very well known dichotomyarising in the behavior of the macroscopic Keller-Segel system is derived atthe kinetic level, being closer to microscopic features. Indeed, under theassumption of spherical symmetry, we prove that solutions with initial data oflarge mass blow-up in finite time, whereas solutions with initial data of smallmass do not. Blow-up is the consequence of a virial identity and the existencepart is derived from a comparison argument. Spherical symmetry is crucialwithin the two approaches. We also briefly investigate the drift-diffusionlimit of such a kinetic model. We recover partially at the limit theKeller-Segel criterion for blow-up, thus arguing in favour of a global linkbetween the two models.

Critical mass phenomenon for a chemotaxis kinetic model with spherically symmetric initial data