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.