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 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