## Analysis and Applied Mathematics Seminar

Trevor Leslie

Illinois Institute of Technology

Limiting configurations for solutions to the 1D Euler Alignment System

**Abstract:**The Euler Alignment system is a hydrodynamic PDE version of the celebrated Cucker-Smale ODE's of collective behavior. Together with Changhui Tan (University of South Carolina), we developed a theory of weak solutions in 1D, which provides a uniquely determined way to evolve the dynamics after a blowup. Inspired by Brenier and Grenier's work on the pressureless Euler equations, we show that the dynamics of interest are captured by a nonlocal scalar balance law, the unique entropy solution of which we generate through a discretization involving the "sticky particle Cucker-Smale" system. In this talk, we will discuss the formation of clusters of mass in the Euler Alignment system, and we will describe how to predict these clusters using the flux from the associated scalar balance law. The main results of this talk can be found in the preprint arXiv:2307.13626 (to appear in the Journal of Evolution Equations).

Monday February 12, 2024 at 4:00 PM in 636 SEO