Asymptotic flocking dynamics of Relativistic-Cucker-Smale particles immersed in incompressible Navier-Stokes equations

Abstract

In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the time-asymptotic behavior of the proposed model in $\mathbb{T}^3$. It is shown that the coupled system exhibits an exponential alignment under some specific assumptions, and that weak solutions exist globally for general initial data.