There will be an invited talk.

Title: **Regularity and Long-Time Behavior for Hydrodynamic Flocking Models**

Speaker: **Prof. Trevor Leslie** (Univ. of Wisconsin-Madison)

Time: **2020 March 10th, 04:00pm~05:00pm**

Place: **27-220**

Abstract:

We consider the Euler Alignment model, a hydrodynamic analog of the discrete Cucker-Smale flocking ODE system. The salient feature of the Cucker-Smale model is the interaction of agents through a so-called “communication protocol” that tends to align the velocities of the agents; this alignment mechanism also drives the Euler Alignment PDEs. We discuss several of the different communication protocols treated in the literature and the corresponding wellposedness theory for the Euler Alignment model in each case. In the case of smooth, bounded protocols in one space dimension, it is possible to completely characterize the initial data leading to the existence of regular solutions, in terms of a certain pointwise balance between the initial velocity and the “total influence” from the density profile. This balance is captured by the sign of a certain quantity that we denote by e. Under the additional assumption of periodicity, a quantity closely related to e determines the long-time distortion of the density profile away from its average value.