Stability of infinite time blow up for the Patlak Keller Segel system

Abstract

We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemo-taxis. When the mass is equal to $8\pi$ and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations.

References in corpus (3)

• Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow
• Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain
• Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model

Cited by in corpus (2)

• On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow
• Stable type II blowup for the 7 dimensional 1-corotational energy supercritical harmonic map heat flow