Hydrodynamic Cucker-Smale model with normalized communication weights and time delay

TL;DR

This paper analyzes a hydrodynamic Cucker-Smale model incorporating time delays and normalized communication, proving global solutions and flocking conditions, and revealing critical phenomena in a one-dimensional setting.

Contribution

It introduces a novel hydrodynamic model with time delay and normalized weights, providing existence, flocking criteria, and critical phenomena analysis.

Findings

Proved existence of global classical solutions.

Derived sufficient conditions for flocking behavior.

Identified critical phenomena in one-dimensional case.

Abstract

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time delayed non-local alignment forces. We resort to its Lagrangian formulation and prove the existence of its global in time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-dimensional setting.