Weak solutions for Euler systems with non-local interactions
Abstract
We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension . These models arise in the study of self-organisation in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of \emph{dissipative} solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction.
Cite
@article{arxiv.1512.03116,
title = {Weak solutions for Euler systems with non-local interactions},
author = {José A. Carrillo and Eduard Feireisl and Piotr Gwiazda and Agnieszka Świerczewska-Gwiazda},
journal= {arXiv preprint arXiv:1512.03116},
year = {2015}
}