Abstract
We construct axially symmetric finite-time blow-up solutions to the three-dimensional Keller–Segel system. By adapting gluing techniques, we derive a precise asymptotic expansion for Type II singularities that generalizes the recent work of Hou, Nguyen, and Song [30]. In our construction the mass concentrates along multiple rings and we obtain a refined expansion for the blow-up rate.
| Original language | English |
|---|---|
| Article number | 111443 |
| Journal | Journal of Functional Analysis |
| Volume | 290 |
| Issue number | 12 |
| Early online date | 9 Mar 2026 |
| DOIs | |
| Publication status | E-pub ahead of print - 9 Mar 2026 |
Data Availability Statement
No data was used for the research described in the article.Funding
The work of F. Buseghin, which began during his PhD studies, is part of the ERC Starting Grant project FloWAS that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 101117820). J. Dávila has been supported by a Royal Society Wolfson Fellowship, UK, Grant RSWF/FT/191007. M. del Pino has been supported by The Royal Society Research Professorship grant RP-R1-180114 and by the ERC/UKRI Horizon Europe grant ASYMEVOL, EP/Z000394/1.
Keywords
- Asymptotic expansion
- Gluing techniques
- Keller-Segel system
- Type II blow-up
ASJC Scopus subject areas
- Analysis
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