Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part II: Fine particles regime

The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes equations. This system is intended to model the evolution of particles interacting with a fluid. The coupling arises from the force terms. The limit problem is the Navier-Stokes system with non constant density. The density which is involved in this system is the sum of the (constant) density of the fluid and of the macroscopic density of the particles. The proof relies on a relative entropy method.