A Sharp Mass Threshold for Boundedness in a Critical Quasilinear Chemotaxis Model With Indirect Signal Production: The Radially Symmetric Case
Year: 2026
Type: preprint
Abstract: A critical quasilinear chemotaxis model with indirect signal production in space dimensions higher than two is studied under radial symmetry. Exploiting the variational structure of the system, the existence of a sharp mass threshold M\textsubscr{c} > 0 is established: all solutions with mass below M\textsubscr{c} are global and bounded, while those with mass above M\textsubscr{c} and sufficiently negative energy are global but blow up in infinite time. Moreover, the value of the critical mass M\textsubscr{c} is related to the best constant of a variant of a Hardy-Littlewood-Sobolev inequality.
Source: arXiv (Cornell University)
Authors: Laurençot, Philippe, Walker, Christoph
Institution: Le LAMA
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208772364