PreprintCC BY 4.0arXiv
Sharp blow-up condition for a two-species cross attraction system in 3 or more dimensions
Abstract
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of free-energy solutions, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a set of critical values: there is a critical value of a parameter pair in the system of equations for which there is a global-in-time energy solution and there exist blowing-up free-energy solutions under a criticality condition is violated for the parameter pair.
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BibTeX
@misc{ulusoy2026sharp,
title = {{Sharp blow-up condition for a two-species cross attraction system in 3 or more dimensions}},
author = {Suleyman Ulusoy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09078},
eprint = {2610.09078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09078},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp blow-up condition for a two-species cross attraction system in 3 or more dimensions
AU - Suleyman Ulusoy
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09078
UR - https://arxiv.org/abs/2610.09078
AB - We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of free-energy solutions, namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a set of critical values: there is a critical value of a parameter pair in the system of equations for which there is a global-in-time energy solution and there exist blowing-up free-energy solutions under a criticality condition is violated for the parameter pair.
ER -