Hydrodynamic limit for compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force

We investigate the hydrodynamic limit of weak solutions to compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force in three-dimensional torus domain. Due to the absence of dissipation terms in particle equation, it is difficult to study this problem. Based on the relative entropy method, it is shown that the global weak solutions of the compressible Navier-Stokes-Vlasov-Poisson equations converge to the smooth solutions of the limiting two-phase fluid model.We obtained that the distribution function $f^{\epsilon}$ converges to a Dirac distribution in velocity, the fluid density $\rho^{\epsilon}$ and velocity $u^{\epsilon}$ converge to $\rho$ and $u$, respectively.