On a fluid-particle interaction model: Global in time weak solutions with in a moving domain in ℝ3

Abstract

A fluid-particle interaction model is presented 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 particles exert mutually. In the present context, the flow occupies a physical domain Gt with boundary Ωt both of which vary in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior and viscosity in the weak formulation.