Collective stochastic dynamics of the Cucker-Smale ensemble under uncertain communication

We study the collective dynamics of the Cucker-Smale (C-S) ensemble under random communication. As the effective modeling of the C-S ensemble with infinite size, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed stochastic kinetic model with a multipl...

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Bibliographic Details
Published in:Journal of Differential Equations 2021-05, Vol.284, p.39-82
Main Authors: Ha, Seung-Yeal, Jung, Jinwook, Röckner, Michael
Format: Article
Language:English
Subjects:
Cucker-Smale model
Emergence
Flocking
Random communication
Stochastic kinetic Cucker-Smale equation
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Summary:We study the collective dynamics of the Cucker-Smale (C-S) ensemble under random communication. As the effective modeling of the C-S ensemble with infinite size, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed stochastic kinetic model with a multiplicative noise, we present a global existence of strong solutions and their asymptotic flocking dynamics, when initial datum is sufficiently regular, and communication weight function has a positive lower bound.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.02.046