Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2020

Fluid models with phase transition for kinetic equations in swarming

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.

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

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  • HAL Id : hal-03591109 , version 1

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