## Abstract

We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsive force limit, we provide evidence of a phase transition from disordered to ordered motion which manifests itself as a change of type of the limit model (from hyperbolic to diffusive) at the crossing of a critical noise intensity. In the hyperbolic regime, the resulting model, referred to as the 'Self-Organized Hydrodynamics (SOH)', consists of a system of compressible Euler equations with a speed constraint. We show that the range of SOH models obtained by this limit is restricted. To waive this restriction, we compute the Navier-Stokes diffusive corrections to the hydrodynamic model. Adding these diffusive corrections, the limit of a large propulsive force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints.

Original language | English |
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Pages (from-to) | 1249-1278 |

Number of pages | 30 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 19 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jul 2014 |

Externally published | Yes |

## Keywords

- Chapman-Enskog expansion
- Cucker-Smale model
- Diffusion
- Hydrodynamic model
- Self-propulsion
- Swarm
- Vicsek model