Convergence of the two‐fluid compressible Navier–Stokes–Poisson system to the incompressible Euler equations

Abstract

In this paper, we consider the combined quasi‐neutral and inviscid limits of the two‐fluid compressible Navier–Stokes–Poisson system in the unbounded domain with the ill‐prepared initial data. We prove that the weak solutions of the compressible Navier–Stokes–Poisson system converge to the strong solution of the incompressible Euler equation as long as the latter exists. Moreover, the convergence rates are also obtained.