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arXiv · 2609.03713

A Sharp Mass Threshold for Boundedness in a Critical Quasilinear Chemotaxis Model With Indirect Signal Production: The Radially Symmetric Case

Philippe Laurençot·Christoph Walker
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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.

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Philippe Laurençot, Christoph Walker. 2026-09-03. A Sharp Mass Threshold for Boundedness in a Critical Quasilinear Chemotaxis Model With Indirect Signal Production: The Radially Symmetric Case. https://arxiv.org/abs/2609.03713

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