Emergence of multi-cluster flocking in the relativistic Cucker-Smale model

We study the multi-cluster flocking for the relativistic Cucker-Smale (RCS) model. To this end, we reformulate the RCS model as a coupled system of multiple subsystems, and derive a system of dissipative differential inequalities on position-velocity averages and deviations. A notable distinction from mono-cluster flocking behavior in RCS is the non-exponential decay rate for micro-velocity, which depends on the spatial decay rate of the communication weight.