Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system

Details Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system

2008-10-19

arxiv.org/abs/0810.3367v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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