From the kinetic theory of gases to models for aerosol flows

This paper proposes two different approaches for deriving the Vlasov-Navier-Stokes (or Vlasov-Stokes) system used in the theory of 'thin' aerosol flows from two kinds of microscopic models. One approach is based on homogenization techniques for elliptic equations in domains with holes, whereas the other approach is based on the various mathematical tools used to study the fluid dynamic limits of the Boltzmann equation.