Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment

TL;DR

This paper studies the long-term behavior of a nonlinear compressible Euler system with velocity alignment, revealing how different nonlinearities and communication protocols lead to emergent flocking phenomena.

Contribution

It introduces a nonlinear extension of the Euler-alignment system and analyzes diverse asymptotic behaviors resulting from various nonlinearities and protocols.

Findings

Alignment and flocking emerge asymptotically

Different nonlinearities produce distinct behaviors

Nonlocal communication influences system dynamics

Abstract

We consider the compressible Euler system with a family of nonlinear velocity alignments. The system is a nonlinear extension of the Euler-alignment system in collective dynamics. We show the asymptotic emergent phenomena of the system: alignment and flocking. Different types of nonlinearity and nonlocal communication protocols are investigated, resulting in a variety of different asymptotic behaviors.