Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system

2025/08/11 by Federico Buseghin, Buseghin, Federico, Juan Dávila +5
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2508.08103

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. In our construction the mass concentrates along multiple rings and we obtain a refined expansion for the blow-up rate.

Citations

• Axisymmetric type II blowup solutions to the three dimensional Keller-Segel system
• Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions
• On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher
• Existence of finite time blow-up in Keller-Segel system
• Construction of type I-Log blowup for the Keller-Segel system in dimensions 3 and 4
• Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher
• Refined description and stability for singular solutions of the 2D\n Keller-Segel system
• Existence and stability of infinite time blow-up in the Keller-Segel system
• Spectral analysis for singularity formation of the two dimensional Keller-Segel system
• Blow-up for the 3-dimensional axially symmetric harmonic map flow into\n S2
• Singularity formation for the two-dimensional harmonic map flow into S²
• Green's function and infinite-time bubbling in the critical nonlinear heat equation
• Uniqueness and long time asymptotic for the Keller-Segel equation: The parabolic-elliptic case
• On the stability of critical chemotactic aggregation
• Asymptotic estimates for the parabolic-elliptic Keller-Segel model in the plane
• On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
• Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
• Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension
• Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk
• Finite-time aggregation into a single point in a reaction - diffusion system
• On explosions of solutions to a system of partial differential equations modelling chemotaxis
• Model for chemotaxis
• A user’s guide to PDE models for chemotaxis

Related

• Axisymmetric type II blowup solutions to the three dimensional Keller-Segel system
• Construction of type I-Log blowup for the Keller-Segel system in dimensions 3 and 4
• Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher
• Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions
• Blow up analysis for Keller-Segel system