KINETIC AND HYDRODYNAMIC MODELS FOR THE RELATIVISTIC CUCKER-SMALE ENSEMBLE AND EMERGENT BEHAVIORS

Abstract

We study emergent behaviors of relativistic kinetic and hydrodynamic models which can be derived from the relativistic Cucker-Smale (RCS) model. The RCS model was introduced to describe the flocking dynamics of relativistic particles in authors' recent work. The proposed relativistic kinetic and hydrodynamic models correspond to relativistic counterparts of the Vlasov-type CS model and pressureless gas dynamics, respectively, and their classical limits can be made in any finite-time interval as the speed of light tends to infinity. For the proposed relativistic models, we provide a global well-posedness of classical solutions and asymptotic flocking estimates using Lyapunov functional approach.