Finite time blow-up for radially symmetric solutions to a critical   quasilinear Smoluchowski-Poisson system
  Finite time blow-up is shown to occur for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system provided that the mass of the initial condition exceeds an explicit threshold. In the supercritical case, blow-up is shown to take place for any positive mass. The proof relies on a novel identity of virial type. 
Tomasz Cie\'slak and Philippe Lauren\c{c}ot