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

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 $8π$ 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.

preprint2016arXivOpen access
Tej-Eddine GhoulNader Masmoudi
math.AP
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Open access2 authors1 topic
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Tej-Eddine GhoulNader Masmoudi

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