Abstract

We construct solutions to the two‐dimensional parabolic‐elliptic Keller‐Segel model for chemotaxis that blow up in finite time T. The solution is decomposed as the sum of a stationary state concentrated at scale λ and of a perturbation. We rely on a detailed spectral analysis for the linearised dynamics in the parabolic neighbourhood of the singularity performed by the authors in [10], providing a refined expansion of the perturbation. Our main result is the construction of a stable dynamics in the full nonradial setting for which the stationary state collapses with the universal law where γ is the Euler constant. This improves on the earlier result by Raphael and Schweyer and gives a new robust approach to so‐called type II singularities for critical parabolic problems. A by‐product of the spectral analysis we developed is the existence of unstable blowup dynamics with speed © 2021 Wiley Periodicals LLC.

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