时间：2017年3月17日 中午12:201:00
地点：华中科技大学创新研究院恩明楼813室
报告人：张雄韬（Seoul National University
题目: UNIFORM MEANFIELD LIMIT FOR THE CS MODEL WITH/WITHOUT NOISE
Abstract. :In this talk, we consider CuckerSmale mdoel (CS) with or without random noise. For CS ocking model without noise, we present a uniform stability of the solutions with respect to the initial data. When coupling between particles is longranged, it is well known that a global (monocluster) ocking con_guration emerges asymptotically and exponentially fast. However, the globalintime stability of such ocking states for the CS model has not been addressed in the literature. As a direct application of the uniform stability, we obtain the uniformintime mean_eld limit from the particle CS model to the kinetic CS model in the Wasserstein metric. While for CS model with a multiplicative noise, We present a new kinetic CuckerSmaleFokkerPlanck (CSFP) type equation with a degenerate di_usion, which describes the dynamics for an ensemble of in_nitely many CuckerSmale particles in a random environment. We present the global existence of classical solutions to the CSFP equation for a su_ciently smooth initial datum without smallness in its size. Moreover, we provide a threshold result depending on the coupling strength.
For the kinetic CSFP equation with a metric dependent communication weight, we provide a uniformintime mean_eld limit from the stochastic CSmodel to the kinetic CSFP equation without convergence rate.
