Recent progress on the mean-field limit of the Cucker-Smale model for flocking

In this paper, we give a brief survey on the state-of-the-art results on the mean-field limit of the Cucker-Smale(CS) model for flocking. The CS model is one of well-studied collective dynamics models. Collective motions of self-propelled particles often appear in our nature. Some collective motions are often described by different types of partial differential equations. We discuss that they fall down to the special cases of the universal nonlinear consensus model at the microscopic level. We also discuss how an interacting particle system with a large size can be effectively approximated by the corresponding mean-field model by the rigorous justification of the mean-field limit. In particular, we focus on the uniform-in-time mean-field limit of the CS model for flocking using the uniform-in-time stability estimate and asymptotic flocking estimates under some framework which guarantees the exponential flocking.