组织者: 邓权灵

Abstract:

We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker-Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type Cucker-Smale equation with spatially nonlocal (convolution) alignment force, our scaling yields a kinetic equation whose alignment field becomes local in space and nonlocal only in velocity. For the spatially homogeneous case, we obtain an explicit solution and derive quantitative flocking rates. For the spatially inhomogeneous equation we establish a local well-posedness in W^{1,\infty} and in C_b^{1,\alpha}, highlighting the additional difficulties caused by the absence of a convolution structure. Moreover, for sufficiently small interaction strength we present a global well-posedness and a forward-in-time L^1 asymptotic completeness property. Finally, we investigate mono-kinetic solutions and exhibit finite-time blow-up scenarios.

Bio:

Jaemoon Lee is a graduate student in the combined M.S./Ph.D. program in the Department of Mathematical Sciences at Seoul National University. He received his bachelor's degrees in Mathematics and Artificial Intelligence from SNU. He conducts research in the HYKE Research Group under Prof. Seung-Yeal Ha, studying collective dynamics models such as Cucker-Smale, Kuramoto, and Motsch-Tadmor.