The quasineutral limit of compressible Navier–Stokes–Poisson system with heat conductivity and general initial data

Abstract

The quasineutral limit of compressible Navier–Stokes–Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier–Stokes–Poisson system converges strongly to the strong solution of the incompressible Navier–Stokes equations plus a term of fast singular oscillating gradient vector fields. Moreover, if the Debye length, the viscosity coefficients and the heat conductivity coefficient independently go to zero, we obtain the incompressible Euler equations. In both cases the convergence rates are obtained.