LAUSR

In this study, we consider a viscous compressible model of plasma and semiconductors, which is expressed as a compressible Navier-Stokes-Poisson equation. We prove that there exists a strong solution to the boundary value problem of the steady compressible Navier-Stokes-Poisson equation with large external forces in bounded domain, provided that the ratio of the electron/ions mass is appropriately small. Moreover, the zero-electron-mass limit of the strong solutions is rigorously verified. The main idea in the proof is to split the original equation into 4 parts, a system of stationary incompressible Navier-Stokes equations with large forces, a system of stationary compressible Navier-Stokes equations with small forces, coupled with 2 Poisson equations. Based on the known results about linear incompressible Navier-Stokes equation, linear compressible Navier-Stokes, linear transport, and Poisson equations, we try to establish uniform in the ratio of the electron/ions mass a priori estimates. Further, using Schauder fixed point theorem, we can show the existence of a strong solution to the boundary value problem of the steady compressible Navier-Stokes-Poisson equation with large external forces. At the same time, from the uniform a priori estimates, we present the zero-electron-mass limit of the strong solutions, which converge to the solutions of the corresponding incompressible Navier-Stokes-Poisson equations.