Existence of finite time blow-up in Keller-Segel system

Federico Buseghin; Juan Davila Bonczos; Manuel Del Pino; Monica Musso

doi:10.1007/s40818-026-00241-7

Existence of finite time blow-up in Keller-Segel system

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system (Formula presented.) We show that there exists ε>0 such that for any m satisfying (Formula presented.) and any k given points q1,..,qk in R2 there is an initial data u0∗ of (∗) for which the solution u(x, t) blows up in finite time as t→T with the approximate profile (Formula presented.) with λj(t)≈2e-γ+22T-te-|ln(T-t)|2 where γ=0.57721.. is the Euler-Mascheroni constant, ξj(t)→qj∈R2 and such that (Formula presented.) This construction generalizes the existence result of the stable blow-up dynamics recently proved in [17, 18].

Original language	English
Article number	17
Number of pages	144
Journal	Annals of PDE
Volume	12
Issue number	1
Early online date	16 May 2026
DOIs	https://doi.org/10.1007/s40818-026-00241-7
Publication status	Published - 16 May 2026

Data Availability Statement

No datasets were generated or analysed during the current study.

Funding

Open access funding provided by CY Cergy Paris Université. Open access funding provided by CY Cergy Paris Université.

Funders
CY Cergy Paris Université

ASJC Scopus subject areas

Analysis
Mathematical Physics
General Physics and Astronomy
Geometry and Topology
Applied Mathematics

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10.1007/s40818-026-00241-7Licence: CC BY

https://arxiv.org/abs/2312.01475

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AU - Buseghin, Federico

AU - Davila Bonczos, Juan

AU - Del Pino, Manuel

AU - Musso, Monica

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Existence of finite time blow-up in Keller-Segel system

Abstract

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