English

Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

Analysis of PDEs 2022-10-31 v1 Mathematical Physics math.MP

Abstract

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.

Keywords

Cite

@article{arxiv.2210.16122,
  title  = {Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies},
  author = {Pierre Degond and Amic Frouvelle and Sara Merino-Aceituno and Ariane Trescases},
  journal= {arXiv preprint arXiv:2210.16122},
  year   = {2022}
}