English

On a two-species cross attraction system in higher dimensions

Analysis of PDEs 2021-11-12 v1

Abstract

We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d3d \geq 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.

Keywords

Cite

@article{arxiv.2111.06154,
  title  = {On a two-species cross attraction system in higher dimensions},
  author = {Eric A. Carlen and Suleyman Ulusoy},
  journal= {arXiv preprint arXiv:2111.06154},
  year   = {2021}
}
R2 v1 2026-06-24T07:34:54.810Z