Mathematical modeling and analysis of Cucker-Smale ensemble in a temperature field

Abstract

In this thesis, we mainly discuss the Thermodynamic Cucker-Smale model<br/> (TCS), a kind of the Cucker-Smale model, that is influenced by the internal<br/> energy of the particles. The TCS model is constructed to satisfy the entropy<br/> condition and other notable thermodynamic behaviors.<br/> We prove that under certain initial conditions, a flocking behavior emerges<br/> in TCS models, the fact from which we further draw the conclusion of the<br/> uniform stability of the TCS models.<br/> We also present mesoscopic and macroscopic versions of the TCS model :<br/> kinetic TCS and hydrodynamic TCS models. Using stability and regularity,<br/> we prove that the solution for each of these models exists for every time.<br/> Also, we show that each of these models has similar flocking behaviors as<br/> those of particle models. Furthermore, we show the well-posedness of each<br/> model.