学术报告
UNIFORM MEAN-FIELD LIMIT FOR THE C-S MODEL WITH/WITHOUT NOISE-Prof. XIONGTAO ZHANG (Seoul National University)
题目：UNIFORM MEAN-FIELD LIMIT FOR THE C-S MODEL WITH/WITHOUT NOISE
报告人：Dr. XIONGTAO ZHANG (Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea)
Abstract：
In this talk, we consider Cucker-Smale mdoel (C-S) with or without random noise. For C-S flocking model without noise, we present a uniform stability of the solutions with respect to the initial data. When coupling between particles is long-ranged, it is well known that a global (mono-cluster) flocking conguration emerges asymptotically and exponentially fast. However, the global-in-time stability of such flocking states for the C-S model has not been addressed in the literature. As a direct application of the uniform stability, we obtain the uniform-in-time mean-field limit from the particle C-S model to the kinetic C-S model in the Wasserstein metric. While for C-S model with a multiplicative noise, We present a new kinetic Cucker-Smale-Fokker-Planck (CS-FP) type equation with a degenerate dif usion, which describes the dynamics for an ensemble of infinitely many Cucker-Smale particles in a random environment. We present the global existence of classical solutions to the CS-FP equation for a sufficiently smooth initial datum without smallness in its size. Moreover, we provide a threshold result depending on the coupling strength. For the kinetic CS-FP equation with a metric dependent communication weight, we provide a uniform-in-time mean-field limit from the stochastic CS-model to the kinetic CS-FP equation without convergence rate.
时间：4月13日(周四) 下午 4:00--5:00
地点：首师大校本部新教二楼524
欢迎全体师生积极参加！
