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Our work deals with the systematic study of the coupling between the nonlocalStokes system and the Vlasov equation. The coupling is due to a drag forcegenerated by the fluid-particles interaction. We establish the existence ofglobal weak solutions for the nonlocal Stokes-Vlasov system in dimensions twoand three without resorting to assumptions on higher-order velocity moments ofthe initial distribution of particles. We then study by the means of thesigma-convergence method, the asymptotic behavior in the general deterministicframework, of the sequence of solutions to the nonlocal Stokes-Vlasov system.In guise of illustration, we provide several physical applications of thehomogenization result including periodic, almost-periodic and weaklyalmost-periodic settings.

Nonlocal Stokes-Vlasov system: Existence and deterministic homogenization results