Fluid models with phase transition for kinetic equations in swarming - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2020

Fluid models with phase transition for kinetic equations in swarming

Mihaï Bostan
  • Fonction : Auteur
  • PersonId : 837137
José Carrillo

Résumé

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.
Fichier principal
Vignette du fichier
main_PhaseTransition_april_2020.pdf (369.69 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03591109 , version 1 (28-02-2022)

Identifiants

  • HAL Id : hal-03591109 , version 1

Citer

Mihaï Bostan, José Carrillo. Fluid models with phase transition for kinetic equations in swarming. Mathematical Models and Methods in Applied Sciences, 2020. ⟨hal-03591109⟩
31 Consultations
15 Téléchargements

Partager

Gmail Facebook X LinkedIn More