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

TL;DR

This paper demonstrates finite time blow-up for radially symmetric solutions of a critical quasilinear Smoluchowski-Poisson system when initial mass exceeds a threshold, and for any positive mass in the supercritical case, using a new virial identity.

Contribution

It introduces a novel virial-type identity to analyze blow-up phenomena in a critical quasilinear Smoluchowski-Poisson system, establishing explicit mass thresholds.

Findings

Finite time blow-up occurs when initial mass exceeds a threshold.

Blow-up occurs for any positive mass in the supercritical case.

A new virial identity is used to prove blow-up results.

Abstract

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.