Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations

This article is devoted to the asymptotic analysis of a system of coupled kinetic and fluid equations, namely the Vlasov-Fokker-Planck equation and a compressible Navier-Stokes equation. Such a system is used, for example, to model fluid-particle interactions arising in sprays, aerosols or sedimentation problems. The asymptotic regime corresponding to a strong drag force and a strong Brownian motion is studied and the convergence toward a two phase macroscopic model is proved. The proof relies on a relative entropy method. A. Mellet was partially supported by NSF grant DMS-0456647.