Global Existence of Strong Solutions to the Kinetic Cucker--Smale Model Coupled with the Stokes Equations

TL;DR

This paper proves the global existence of strong solutions for a coupled kinetic Cucker--Smale and Stokes equations model in an unbounded domain, using weighted Sobolev spaces and space-time estimates without initial data restrictions.

Contribution

It provides a comprehensive analysis demonstrating global-in-time strong solutions for the coupled model without smallness assumptions on initial data.

Findings

Established global existence of strong solutions

Used weighted Sobolev spaces and space-time estimates

No smallness condition on initial data required

Abstract

In this paper, we investigate existence of global-in-time strong solutions to the kinetic Cucker--Smale model coupled with the Stokes equations in the whole space. By introducing a weighted Sobolev space and using space-time estimates for the linear non-stationary Stokes equations, we present a complete analysis on existence of global-in-time strong solutions to the coupled model, without any smallness requirements on initial data.