2023 Wilmington NC USA

Nonlinear models in kinetic theory, collective behavior, and fluid dynamics

 Organizer(s):
Name:
Affiliation:
Country:
Christopher Henderson
University of Chicago
USA
Stanley Snelson
Florida Institute of Technology
USA
Andrei Tarfulea
Louisiana State University
USA
 Abstract:  
  This special session will address the modeling aspects and mathematical theory of physical and biological phenomena described by mesoscopic limits of small-scale systems. In particular, the focus is on the interrelated classes of kinetic and fluid dynamics equations and models for collective behavior. These models often feature long-range interactions, leading to nonlocal terms in the corresponding equations. Examples arise in subsonic hydrodynamics (pressure ``communicates`` much faster than fluid motion), biology (population and genetic drift arising from jump processes, as well as ``flocking`` in swarm dynamics), and plasma physics (characterized by high-velocity, strongly interacting ion motion). Such models involve novel mathematical challenges in deriving the limiting equations and determining their behavior quantitatively.