##### 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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