Global weak solution to the inhomogeneous Navier–Stokes–Vlasov equations

The inhomogeneous Navier–Stokes–Vlasov equations for fluid-particle flows are considered in the three-dimensional space. The coupling in the fluid-particle system 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 initial data. The existence of global weak solution is established through an approximation scheme, a fixed point argument, energy estimates, and a weak convergence method.