English

Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel

Analysis of PDEs 2023-09-06 v1

Abstract

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in [2] to the Cauchy problem for any BVBV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.

Keywords

Cite

@article{arxiv.2309.01939,
  title  = {Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel},
  author = {Debora Amadori and Cleopatra Christoforou},
  journal= {arXiv preprint arXiv:2309.01939},
  year   = {2023}
}

Comments

31 pages, 2 figures

R2 v1 2026-06-28T12:12:43.990Z