Abstract:
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.
Key words and phrases:Navier–Stokes equation, Fokker–Planck equation, Poisson equation, global weak solution, modified Galerkin method, fixed point Schauder theorem, compactness of approximations.