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Uniform stability of the relativistic Cucker-Smale model and its application to a mean-field limit

Cited 9 time in Web of Science Cited 9 time in Scopus
Authors

Ahn, Hyunjin; Ha, Seung-Yeal; Kim, Jeongho

Issue Date
2021-12
Publisher
American Institute of Mathematical Sciences
Citation
Communications on Pure and Applied Analysis, Vol.20 No.12, pp.4209-4237
Abstract
ABSTRACT. We present a uniform(-in-time) stability of the relativistic CuckerSmale (RCS) model in a suitable framework and study its application to a uniform mean-field limit which lifts earlier classical results for the CS model in a relativistic setting. For this, we first provide a sufficient framework for an exponential flocking for the RCS model in terms of the diameters of state observables, coupling strength and communication weight function, and then we use the obtained exponential flocking estimate to derive a uniform lq,pstability of the RCS model under appropriate conditions on initial data and system parameters. As an application of the derived uniform lq,p-stability estimate, we show that a uniform mean-field limit of the RCS model can be made for some admissible class of solutions uniformly in time. This justifies a formal derivation of the kinetic RCS equation [18] in a rigorous setting.
ISSN
1534-0392
URI
https://hdl.handle.net/10371/180058
DOI
https://doi.org/10.3934/cpaa.2021156
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