PDE Seminar: Unidirectional Alignment Dynamics

Trevor Leslie, Illinois Institute of Technology Title: Unidirectional Alignment Dynamics Abstract: In this talk, we discuss the wellposedness and long-time behavior of the pressureless Euler Alignment system, which arises as a hydrodynamic limit of the Cucker-Smale ODEs of collective behavior. After a brief orientation on the role of the alignment mechanism in the equations, we will discuss the existing 1D theory, the challenges presented by the multidimensional setting, and the special but instructive scenario of unidirectional dynamics, focusing on my recent joint work with Joshua Adeleke o…