We study collision avoidance and flocking dynamics for the relativistic Cucker–Smale (RCS) model with a singular communication weight. For a bounded and regular communication weight, RCS particles can exhibit collisions in finite time depending on the geometry of the initial configuration. In contrast, for a singular communication weight, when particles collide, the associated Cucker–Smale vector field becomes unbounded and the standard Cauchy–Lipschitz theory cannot be applied so that existence theory after collisions is problematic. Thus, the collision avoidance problem is directly linked to the global solvability of the singular RCS model and asymptotic flocking dynamics. In this paper, we present sufficient frameworks leading to the nonexistence of finite-time collisions and asymptotic flocking in terms of initial configuration and blow-up rate at the singular point of communication weight.
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January 2022
Research Article|
January 13 2022
Asymptotic flocking dynamics of a relativistic Cucker–Smale flock under singular communications
Junhyeok Byeon
;
Junhyeok Byeon
a)
1
Department of Mathematical Sciences, Seoul National University
, Seoul 08826, Republic of Korea
a)Author to whom correspondence should be addressed: giugi2486@snu.ac.kr
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Seung-Yeal Ha
;
Seung-Yeal Ha
b)
2
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University
, Seoul 08826, Republic of Korea
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Jeongho Kim
Jeongho Kim
c)
3
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University
, Seoul 04763, Republic of Korea
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a)Author to whom correspondence should be addressed: giugi2486@snu.ac.kr
b)
Email: syha@snu.ac.kr
c)
Email: jeonghokim206@gmail.com
J. Math. Phys. 63, 012702 (2022)
Article history
Received:
July 08 2021
Accepted:
December 30 2021
Citation
Junhyeok Byeon, Seung-Yeal Ha, Jeongho Kim; Asymptotic flocking dynamics of a relativistic Cucker–Smale flock under singular communications. J. Math. Phys. 1 January 2022; 63 (1): 012702. https://doi.org/10.1063/5.0062745
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