Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions
Year: 2026
Type: preprint
Abstract: 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 $N \geq 10$. In particular, we exhibit the differences of the criteria between the cases $N \geq 11$ 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.
Source: arXiv (Cornell University)
Authors: Naito, Yūki, Senba, Takasi
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204914540