# Collective stochastic dynamics of the Cucker-Smale ensemble under uncertain communications

## TL;DR

This paper studies the collective behavior of the Cucker-Smale model under uncertain communication channels, introducing a stochastic kinetic equation with noise, and proves well-posedness and flocking behavior.

## Contribution

It introduces a stochastic kinetic Cucker-Smale model with multiplicative noise and establishes global well-posedness and flocking dynamics under certain conditions.

## Key findings

- Proves global well-posedness of the stochastic model.
- Demonstrates asymptotic flocking behavior.
- Establishes conditions for regular initial data and positive lower bounds on communication weights.

## Abstract

We present collective dynamics of the Cucker-Smale (C-S) ensemble under random communications. As an effective modeling of the C-S ensemble, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed stochastic kinetic model with a multiplicative noise, we present a global well-posedness of strong solutions and their asymptotic flocking dynamics, when initial datum is sufficiently regular, and communication weight function has a positive lower bound.