Local well-posedness for the compressible Navier-Stokes-BGK model in Sobolev spaces with exponential weight

Abstract: Sprays are complex flows constituted of dispersed particles in an underlying gas. In this paper, we are interested in the equations for moderately thick sprays consisting of the compressible Navier-Stokes equations and Boltzmann BGK equation. Here the coupling of two equations is through a friction (or drag) force which depends on the density of compressible fluid and the relative velocity between particles and fluid. For the Navier-Stokes-BGK system, we establish the existence and uniqueness of solutions in Sobolev spaces with exponential weight.