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PreprintarXiv licencearXiv

Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions

  • Yūki Naito
  • Takasi Senba
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Abstract

We study the simplest parabolic-elliptic model of chemotaxis in bf RN, and show the optimal criteria for the existence of infinite time blow-up of solutions with the initial data below the Chandrasekhar singular solution when N ≥ 10. In particular, we exhibit the differences of the criteria between the cases N ≥ 11 and N = 10. Our argument is based on the study of the Cauchy problem for the transformed equation involving the averaged mass of the solution and the asymptotic expansions of solutions to the Liouville equation.

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Cite

BibTeXRIS
BibTeX
@misc{naito2026infinite,
  title = {{Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions}},
  author = {Yūki Naito and Takasi Senba},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29522},
  eprint = {2608.29522},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29522},
}
RIS
TY  - UNPB
TI  - Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions
AU  - Yūki Naito
AU  - Takasi Senba
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29522
UR  - https://arxiv.org/abs/2608.29522
AB  - We study the simplest parabolic-elliptic model of chemotaxis in bf R^N, and show the optimal criteria for the existence of infinite time blow-up of solutions with the initial data below the Chandrasekhar singular solution when N ≥ 10. In particular, we exhibit the differences of the criteria between the cases N ≥ 11 and N = 10. Our argument is based on the study of the Cauchy problem for the transformed equation involving the averaged mass of the solution and the asymptotic expansions of solutions to the Liouville equation.
ER  -