Global weak solutions to the inhomogeneous Navier-Stokes-Vlasov equations

A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the Vlasov equation. An initial-boundary value problem is studied in a bounded domain with large data. The existence of global weak solutions is established through an approximation scheme, energy estimates, and weak convergence.