Quasi-neutral and zero-viscosity limits of Navier-Stokes-Poisson equations in the half-space

The present paper is concerned with the quasi-neutral and zero-viscosity limits of Navier-Stokes-Poisson equations in the half-space. We consider the Navier-slip boundary condition for velocity and Dirichlet boundary condition for electric potential. By means of asymptotic analysis with multiple scales, we construct an approximate solution of the Navier-Stokes-Poisson equations involving two different kinds of boundary layer, and establish the linear stability of the boundary layer approximations by conormal energy estimate.