报告题目：Weak flocking of phase-spatially extended kinetic Cucker-Smale model

报 告 人：Seung-Yeal Ha 教授（韩国首尔国立大学）

报告时间：2025年6月18日（星期三）09:00—10:00

报告地点：数学科学学院114（小报告厅）      

校内联系人：董久刚 教授         联系方式：84708351-8318

报告摘要：In this talk, we present the emergent behaviors of the weak solutions to the kinetic Cucker-Smale (in short KCS) model in a non-compact spatial-velocity support setting. Unlike the compact support situation, non-compact support of a weak solution can cause a communication weight to have zero lower bound. This causes  previous approach based on the nonlinear functional approach for spatial and velocity diameters to break down. To overcome this difficulty, we derive refined estimates on the upper bounds for the second-order spatial-velocity moments and show the uniqueness of the weak solution using the estimate on the deviation of particle trajectories. For the estimate of emergent dynamics, we consider two classes of distributions functions with decaying properties (an exponential decay or polynomial decay) in phase space, and then verify that the second moment for the velocity deviation from an average velocity tends to zero asymptotically fast, while   second moment for spatial deviation from the center of mass remains  bounded uniformly in time. This illustrates the robustness of the mono-cluster flocking dynamics of the KCS model even for non-compact support settings in phase space and generalizes earlier results on flocking dynamics in a compact support setting. This is a jointwork with Dr. Xinyu Wang (Seoul National University).

报告人简介：Professor Seung Yeal Ha is a professor at the Department of Mathematical Sciences, Seoul National University in Korea since 2003. He was born in Jeonju of Jeonbuk Province on April 1st of 1971. He received a B.S. degree with Summa cum Laude from Seoul National University in 1997 and Ph.D. degree from Stanford University in 2001. After two and half year post-doc experience at Univ. of Wisconsin-Madison right after his Ph.D., he has been working for Seoul National University. Ha’s primary research interests are applied nonlinear analysis such as hyperbolic conservation laws, the kinetic theory of gases and collective dynamics of many-body interacting systems, application of flocking theory to finance and sociology. To date, he has written more than three hundred research papers. He has received numerous honors and awards including 14th Presidential Young Scientist Award in 2010, 17th Korea Science Prize in 2017 and KSIAM-Kumkok prize in 2023. He has given several distinguished lectures in the past such as a plenary talk at 1st AMC(Asian Mathematics Conference) in 2013, and invited talk at ICM 2014 in Seoul, and a plenary talk at HYP 2014 (the largest conference in the hyperbolic problems) and keynote lecture at 32nd International Symposium on Rarefied Gas Dynamics in 2022. He is currently a member of the Korean Academy of Science and Technology.