Seminar series
Date
Mon, 01 Dec 2025
Time
16:30 -
17:30
Location
L4
Speaker
Dowan Koo
Organisation
Mathematical Institute University of Oxford
In this talk, I will introduce the hydrodynamic Euler–Alignment model, focusing on the pressureless case coupled with nonlocal interaction forces, and discuss its large-time dynamics—namely, the emergence of flocking and the characterization of its asymptotic behavior.
New flocking estimates will be presented, showing how the confining effect of nonlocal interaction can, in certain regimes, replace the role of velocity alignment.
The quantitative analysis of the asymptotic behavior will also be discussed. Overall, the convergence rate depends only on the local behavior of the communication weight: bounded kernels lead to exponential decay, while weakly singular ones yield algebraic rates. This reveals a sharp transition in decay rates driven solely by the local singularity of the communication kernel, a regime that had remained largely unexplored.
This talk is based on joint work with José Carrillo (University of Oxford), Young-Pil Choi (Yonsei University), and Oliver Tse (Eindhoven University of Technology).