Coupled Self-Organized Cucker–Smale Hydrodynamics and Navier–Stokes Model for Suspensions of Active Particles

This paper considers the well-posedness of a new kinetic-fluid coupled system describing the self-organized phenomenon in a viscous flow, which contains a Cucker–Smale model with a confining potential at the kinetic level and the Navier–Stokes equation at the hydrodynamic level. We establish the local existence and uniqueness for smooth solutions to this coupled system. The proof relies on two key ingredients. One is to construct an appropriate iteration scheme, in which the proper choice for the normalized mean orientation plays an important role. The second key point is to show the persistence property for the first-order momentum, preventing the possible singularity.