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arXiv · 1610.00456

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

Tej-Eddine Ghoul·Nader Masmoudi
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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.

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Tej-Eddine Ghoul, Nader Masmoudi. 2016-10-03. Stability of infinite time blow up for the Patlak Keller Segel system. https://arxiv.org/abs/1610.00456

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