Zero‐electron‐mass limit of the two‐dimensional compressible Navier‐Stokes‐Poisson equations in bounded domain

Abstract

In this paper, we consider the zero‐electron‐mass limit of the solutions for the two‐dimensional compressible Navier‐Stokes‐Poisson system in the bounded spatial domain. We first show local existence of the regular solutions for the initial boundary value problem to the two‐dimensional compressible Navier‐Stokes‐Poisson equations. Then we establish the uniform estimate of global regular solutions to the compressible Navier‐Stokes‐Poisson equations with well‐prepared initial date for all time. This estimate that is uniform both in time and in the electron mass is derived by a differential inequality with certain decay property. Further, we obtain the global existence of the regular solutions to the compressible Navier‐Stokes‐Poisson equations. Moreover, we also show that the global regular solutions of the initial boundary value problem for the compressible Navier‐Stokes‐Poisson equations converge to the solutions of the incompressible Navier‐Stokes equations as the electron mass tends to zero.