A global existence of classical solutions to the hydrodynamic Cucker-Smale model in presence of a temperature field

We present a hydrodynamic model for the ensemble of thermodynamic Cucker-Smale (TCS) particles in the presence of a temperature field, and study its global-in-time well-posedness in Sobolev space. Our hydrodynamic model can be formally derived from the kinetic TCS model under the mono-kinetic ansatz, and can be viewed as a pressureless gas dynamics with non-local flocking forces. For the global-in-time well-posedness, we assume that communication weight functions are non-negative and non-increasing in their arguments and initial data satisfy non-vacuum conditions and suitable regularity in Sobolev space. In this setting, we use the method of energy estimates and obtain the global existence of classical solutions in any finite time interval. We also present an asymptotic flocking estimate using the Lyapunov functional approach.