Asymptotic limits of the full Navier–Stokes–Fourier–Poisson system

The combined quasineutral and zero-electron-mass limit of the full Navier–Stokes–Fourier–Poisson system in the torus Td (d⩾1) is considered. It is showed that, for well-prepared initial data, the weak solutions of the full Navier–Stokes–Fourier–Poisson system converge to the strong solution of the incompressible Navier–Stokes equations, as long as the latter exists. Moreover, the convergence rates are obtained.