Seminars

UNIFORM MEAN-FIELD LIMIT FOR THE C-S MODEL WITH/WITHOUT NOISE

Author:Administrator    Publicsh date:2017-03-13    Clicks:321
时间:2017年3月17日 中午12:20-1:00 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 MEAN-FIELD LIMIT FOR THE C-S MODEL WITH/WITHOUT NOISE Abstrac ......
时间:2017年3月17日 中午12:20-1:00
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 MEAN-FIELD LIMIT FOR THE C-S MODEL WITH/WITHOUT NOISE
Abstract. :In this talk, we consider Cucker-Smale mdoel (C-S) with or without random noise. For C-S ocking 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) ocking con_guration emerges asymptotically and exponentially fast. However, the global-in-time stability of such ocking 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-_eld 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 di_usion, which describes the dynamics for an ensemble of in_nitely many Cucker-Smale particles in a random environment. We present the global existence of classical solutions to the CS-FP 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 CS-FP equation with a metric dependent communication weight, we provide a uniform-in-time mean-_eld limit from the stochastic CS-model to the kinetic CS-FP equation without convergence rate.