16:10-16:30 Tuesday, 6 May 2025 Auditorium, Rectorate
Abstract
The goal of this talk is to present the multi-scale theory for a new model of alignment, called the s-model. The s-model generalizes the Cucker-Smale model by allowing for a broader class of velocity averaging protocols, while preserving the 1D conservation law, $\partial_t e + \partial_x(ue) = 0$, $e = \partial_x u + s$, which plays a critical role in the regularity theory as well as the long-time behavior. We will present our results on the mean field and hydrodynamic passage between all scales of description as well as the long-time behavior.