On the dynamics of charged particles in an incompressible flow: From kinetic-fluid to fluid–fluid models

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