Propagation of chaos and hydrodynamic description for topological models

TL;DR

This paper proves propagation of chaos and derives a hydrodynamic limit for a topological Cucker-Smale model, connecting microscopic particle interactions to macroscopic fluid-like equations.

Contribution

It provides a rigorous analysis of the topological Cucker-Smale model, establishing propagation of chaos and deriving hydrodynamic equations from particle dynamics.

Findings

Propagation of chaos is established for the model.

A pressureless Euler-type system is derived as the hydrodynamic limit.

The work connects microscopic and macroscopic descriptions of topological interactions.

Abstract

In this work, we study the deterministic Cucker-Smale model with topological interaction. Focusing on the solutions of the corresponding Liouville equation, we show that propagation of chaos holds. Moreover, considering monokinetic solutions, we also obtain a rigorous derivation of the hydrodynamic description given by a pressureless Euler-type system.