  Our work deals with the systematic study of the coupling between the nonlocal
Stokes system and the Vlasov equation. The coupling is due to a drag force
generated by the fluid-particles interaction. We establish the existence of
global weak solutions for the nonlocal Stokes-Vlasov system in dimensions two
and three without resorting to assumptions on higher-order velocity moments of
the initial distribution of particles. We then study by the means of the
sigma-convergence method, the asymptotic behavior in the general deterministic
framework, of the sequence of solutions to the nonlocal Stokes-Vlasov system.
In guise of illustration, we provide several physical applications of the
homogenization result including periodic, almost-periodic and weakly
almost-periodic settings.
