  In this paper, we are interested in the dynamics of charged particles
interacting with the incompressible viscous flow. More precisely, we consider
the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the
incompressible Navier-Stokes system through the drag force. For the proposed
kinetic-fluid model, we study the asymptotic regime corresponding to strong
local alignment and diffusion forces. Under suitable assumptions on the initial
data, we rigorously derive a coupled isothermal/pressureless Euler-Poisson
system and incompressible Navier-Stokes system(in short, EPNS system). For this
hydrodynamic limit, we employ the modulated kinetic energy estimate together
with the relative entropy method and the bounded Lipschitz distance. We also
construct a global-in-time strong solvability for the isothermal/pressureless
EPNS system. In particular, this global-in-time solvability gives the estimates
of hydrodynamic limit hold for all time.
