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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.

List of approved abstract
Name	Affiliation	Title
Ioakeim Ampatzoglou	New York University	Moment estimates and global well-posedness for the binary-ternary Boltzmann equation
Stephen P Cameron	Courant Institute	Critical local-wellposedness for the fully nonlinear Peskin problem
Bin Cheng	University of Surrey	Global weak solutions to a hybrid Vlasov-MHD model for plasma dynamics
William Golding	University of Texas at Austin	Global-in-time well-posedness of the homogeneous Landau-Coulomb equation for small $L^p$ initial data
Laurent Lafleche	Institut Camille Jordan, CNRS and University Lyon 1	Fractional Hypocoercivity
Amelie Loher	University of Cambridge	Regularity Theory for kinetic integro-differential equations
Logan Stokols	Duke University	Continuity for Nonlocal Hypoelliptic Kinetic Equations
Padmanabhan Sundar	Louisiana State University	The Boltzmann process: Existence and construction
Changhui Tan	University of South Carolina	Collective behaviors in macroscopic swarming dynamics
Andrea Tosin	Politecnico di Torino	Macroscopic Limits of Non-Local Kinetic Descriptions of Consensus and Relaxation Dynamics
Weinan Wang	University of Arizona	Well-posedness and Gevrey regularity of some electrodiffusion models
Yuzhe Zhu	University of Cambridge	Boundary regularity for kinetic equations