Global Weak Solutions of the Navier–Stokes/Fokker–Planck/Poisson Linked Equations

We consider the initial boundary value problem for the linked Navier–Stokes/Fokker–Planck/Poisson equations describing the flow of a viscous incompressible fluid with highly dispersed infusion of solid charged particles which are subjected to a random impact from thermal motion of the fluid molecules. We prove the existence of global weak solutions for the problem and study some properties of these solutions.