Global weak solutions to the inhomogeneous incompressible Navier–Stokes–Vlasov–Boltzmann equations

Abstract

In this paper, the initial–boundary value problem of the coupled inhomogeneous incompressible Navier–Stokes equations and Vlasov–Boltzmann equation for the moderately thick spray is considered in three-dimensional space. The global existence of weak solutions is established by an approximation scheme, a fixed point argument and the weak convergence method.