Global solutions for the one-dimensional compressible Navier-Stokes-Smoluchowski system

In this paper, we consider a fluid-particle interaction model for the evolution of particles dispersed in a fluid. The fluid flow is governed by the Navier-Stokes equations for a compressible fluid while the evolution of the particle densities is given by the Smoluchowski equation. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually. We establish the existence and uniqueness of a global classical solution, the existence of weak solutions, and the existence of a unique strong solution of this system in 1D for initial data rho(0) without vacuum states. Published by AIP Publishing.