Quasi-neutral limit of the full Navier–Stokes–Fourier–Poisson system

The quasi-neutral limit of the full Navier–Stokes–Fourier–Poisson system in the torus TdTd (d≥1d≥1) is considered. We rigorously prove that as the scaled Debye length goes to zero, the global-in-time 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. In particular, the effect of large temperature variations is taken into account.