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

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.