Title: Mean-Field Limit for the Cucker-Smale Model I: Regular Case
Speaker: Taoxiong Zhang (Huazhong University of Science and Technology)
Time: 14:30-15:30, October10
Location: Room 201，Ming De Building
Abstract: We introduce the rigorous mean field limit from Cucker-Smale model (CS) to kinetic CS model (KCS) with regular and singular interaction respectively. For regular interaction, the global-in-time stability of flocking states will be addressed. As a direct application of the uniform stability, we obtain the uniform-in-time mean-field limit in the Wasserstein metric. While for C-S model with singular interaction, uniform stability has not been obtained so far, and we will present a probabilistic approach for derivation of the KCS equation from the particle CS model with singular communication. More precisely, we introduce a suitable cutoff in the communication weight, and derive the estimates of the difference between particle trajectory and the kinetic trajectory for cutoff equations. Then we show the cutoff will tends to zero when particle number N tends to infinity and thus verify the mean field limit.
