On the interactions of a flocking ensemble with the Navier-Stokes flow in an infinite channel

Abstract

We study the global existence of weak solutions and asymptotic flocking behavior for the Cucker-Smale-Navier-Stokes (CS-NS) system in an infinitely long cylindrical domain under no-slip and specular reflection boundary conditions. This coupled kinetic-fluid system provides the modeling for the collective dynamics of flocking particles immersed in an incompressible viscous fluid, where the specular boundary condition allows elastic particle-wall interactions. We extend our previous results on Stokes-type coupled systems to the Navier-Stokes regime and establish global weak solutions. In particular, we verify asymptotic convergence toward flocking states. To the best of our knowledge, this is new for kinetic-fluid models with boundary walls. Furthermore, we perform numerical simulations under inflow-outflow boundary conditions to validate analytic results and compare the long-time dynamics of CS-NS with its Stokes counterpart. These simulations illustrate that fluid-particle coupling and inter-particle communication enhance apparent shear-thinning, non-Newtonian flow behaviors, and we compare these findings with shear-thinning phenomena measured in real suspensions of orientable particles, such as blood and swimming bacteria.