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张雄韬——Mean-Field Limit for the Cucker-Smale Model II: Singular Case
发布人:许全华  发布时间:2019-10-09   浏览次数:91

题目Mean-Field Limit for the Cucker-Smale Model II: Singular Case


报告人:张雄韬(华中科技大学)


时间:10月10日,15:30-16:30


地点:明德楼B区201学术报告厅


摘要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.