中央研究院數學研究所

Analysis Seminar

Emergent dynamics of spatially extended relativistic kinetic Cucker-Smale model

2026/04/07 (Tue.) 10:00~13:00

Date : 2026/04/07 (Tue.) 10:00~13:00
Location : online
Speaker : Xinyu Wang (Seoul National University)
Organizer : Tai-Ping Liu (AS)
Abstract : We study the emergent dynamics of the relativistic kinetic Cucker--Smale (RKCS) model without assuming compactness assumptions on spatial and velocity supports. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment force can be zero, so that the previous approach based on the energy method does not provide a quantitative flocking estimate. To overcome this difficulty, we introduce a suitable decay ansatz for the one-particle distribution function and an effective domain by identifying a time-varying region in which the total mass outside of it decays to zero asymptotically. Using these ingredients, we show that weak flocking dynamics emerges asymptotically in the sense that the second moment for velocity fluctuations around the velocity average tends to zero, whereas the second moment for spatial fluctuations around the center of mass remains uniformly bounded in time. Our results demonstrate the robustness of the emergent dynamics in the RKCS model across various non-compact, physically important distributions, including Gaussian distributions, sub-Gaussian distributions, and those with a finite D-th moment.