Nonlocal Stokes-Vlasov system: Existence and deterministic homogenization results

Abstract

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.