Department of Mathematics,
University of California San Diego
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Math 248 - Analysis Seminar
Roman Shvydkoy
UIC
Global hypocoercivity of Fokker-Planck-Alignment equations
Abstract:
In this talk we will discuss a new approach to the problem of emergence in hydrodynamic systems of collective behavior. The problem seeks to establish convergence to a flocking state in a system with self-organization governed by strictly local laws of communication. The typical results in this direction insist on propagation of flock connectivity which translates into a quantitative non-vacuum condition on macroscopic level. With the introduction of small noise one can relax such a condition considerably, and even allow for vacuum, in the context of the corresponding Fokker-Planck-Alignment equations. The flocking behavior becomes the problem of establishing hypocoercivity and relaxation of solutions to the global Maxwellian. We will describe a model which does precisely that in the non-perturbative settings.
April 12, 2022
11:00 AM
https://ucsd.zoom.us/j/
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