Multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint under a singular kernel

Abstract

<abstract><p>This paper presents several sufficient frameworks for multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint (in short, TCSUS) under a singular kernel. By providing precise estimates and deriving the dissipative structure of TCSUS, it was proved that under specific well-prepared conditions for particle positions and fully separated initial velocities, multi-cluster flocking occurs in the TCSUS system under a strong singular kernel. Furthermore, the velocities and temperatures converge to the average final data for each cluster group.</p></abstract>