The Local Existence and Blowup Criterion for Strong Solutions to the Kinetic Cucker--Smale Model Coupled with the Compressible Navier--Stokes Equation

TL;DR

This paper proves local existence and uniqueness of strong solutions for a coupled kinetic and fluid dynamic system, and analyzes the conditions leading to solution blowup, advancing understanding of complex fluid-collective behavior interactions.

Contribution

It introduces a novel analysis of the coupled kinetic Cucker--Smale and compressible Navier--Stokes system, including a blowup criterion and existence results.

Findings

Established local strong solution existence and uniqueness.

Identified blowup mechanisms for the coupled system.

Provided conditions under which solutions may become singular.

Abstract

In this paper, we establish the existence and uniqueness of local strong solutions to the kinetic Cucker--Smale model coupled with the isentropic compressible Navier--Stokes equation in the whole space. Moreover, the blowup mechanism for strong solutions to the coupled system is also investigated.