Slow flocking dynamics of the Cucker-Smale ensemble with a chemotactic movement in a temperature field

Abstract

We study slow flocking phenomenon arising from the dynamics of Cucker-Smale (CS) ensemble with chemotactic movements in a self-consistent temperature field. For constant temperature field, our situation reduces to the previous CS model with chemotactic movements. When a large CS ensemble with chemotactic movements is placed in a self-consistent temperature field, the dynamics of the CS ensemble can be eectively described by the kinetic thermodynamic CS (TCS) equation with chemotactic movements, which corresponds to the coupled collisional transport-reaction diusion system. For the proposed coupled model, we provide a global solvability of strong solutions and their asymptotic flocking estimates which exhibit slow algebraic relaxation toward the flocking state. Our analytical results show that asymptotic flocking is robust with respect to a small perturbation of a constant temperature. © 2020 American Institute of Mathematical Sciences.