Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System

  title={Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System},
  author={Charles Collot and Tej-eddine Ghoul and Nader Masmoudi and Van Tien Nguyen},
  journal={arXiv: Analysis of PDEs},
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 $\lambda$ and of a perturbation. We rely on a detailed spectral analysis for the linearized dynamics in the parabolic neighbourhood of the singularity performed by the authors, providing a refined expansion of the perturbation. Our main result is the construction of a stable dynamics… 
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