Global weak solutions to the compressible Cucker-Smale-Navier-Stokes system in a bounded domain

TL;DR

This paper proves the global existence of weak solutions for a coupled kinetic-fluid model describing flocking particles interacting with a viscous fluid in a bounded domain, using a compressible Navier-Stokes framework.

Contribution

It establishes the first global existence result for weak solutions to this coupled Cucker-Smale-Navier-Stokes system with nonhomogeneous boundary conditions.

Findings

Global weak solutions exist for the system when the adiabatic coefficient exceeds 3/2.

The model captures the interaction between flocking particles and viscous fluid dynamics.

The analysis extends the mathematical understanding of coupled kinetic-fluid systems in bounded domains.

Abstract

A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic Cucker-Smale equation and a compressible Navier-Stokes system with nonhomogeneous boundary conditions. The global existence of weak solutions to this system with adiabatic coefficient $\gamma> {3}/{2}$ is established.