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The mean-field limit of the Cucker-Smale model on complete Riemannian manifolds
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Cited 7 time in Scopus
- Authors
- Issue Date
- 2022-09
- Publisher
- Brown University
- Citation
- Quarterly of Applied Mathematics, Vol.80 No.3, pp.403-450
- Abstract
- We study the mean-field limit of the Cucker-Smale (C-S) model for flocking on complete smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold C-S model on manifolds using the BBGKY hierarchy and derive several a priori estimates on emergent dynamics. Then, we present a rigorous mean-field limit from the particle model to the corresponding kinetic model by using the generalized particle-in-cell method. As a byproduct of our rigorous mean-field limit estimate, we also establish a global existence of a measure-valued solution for the derived kinetic model. Compared to the corresponding results on Rd, our procedure requires additional assumption on holonomy and proper a priori bound on the derivative of parallel transports. As a
- ISSN
- 0033-569X
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