PreprintCC BY 4.0HAL
A SHARP MASS THRESHOLD FOR BOUNDEDNESS IN A CRITICAL QUASILINEAR CHEMOTAXIS MODEL WITH INDIRECT SIGNAL PRODUCTION: THE RADIALLY SYMMETRIC CASE
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 Mc > 0 is established: all solutions with mass below Mc are global and bounded, while those with mass above Mc and sufficiently negative energy are global but blow up in infinite time. Moreover, the value of the critical mass Mc is related to the best constant of a variant of a Hardy-Littlewood-Sobolev inequality.
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BibTeX
@misc{laurencot2026sharp,
title = {{A SHARP MASS THRESHOLD FOR BOUNDEDNESS IN A CRITICAL QUASILINEAR CHEMOTAXIS MODEL WITH INDIRECT SIGNAL PRODUCTION: THE RADIALLY SYMMETRIC CASE}},
author = {Philippe Laurençot and Christoph Walker},
howpublished = {HAL},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2609.03713},
eprint = {2609.03713},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05732257v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A SHARP MASS THRESHOLD FOR BOUNDEDNESS IN A CRITICAL QUASILINEAR CHEMOTAXIS MODEL WITH INDIRECT SIGNAL PRODUCTION: THE RADIALLY SYMMETRIC CASE
AU - Philippe Laurençot
AU - Christoph Walker
PY - 2026
DA - 2026/08/31
PB - HAL
DO - 10.48550/arxiv.2609.03713
UR - https://hal.science/hal-05732257v2
AB - 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 Mc > 0 is established: all solutions with mass below Mc are global and bounded, while those with mass above Mc and sufficiently negative energy are global but blow up in infinite time. Moreover, the value of the critical mass Mc is related to the best constant of a variant of a Hardy-Littlewood-Sobolev inequality.
ER -