Quasineutral limit of Euler-Poisson system with and without viscosity

The quasineutral limit of Euler-Poisson system with and without viscosity in plasma physics in the torus T-d, d greater than or equal to l is studied. That quasineutral regimes are the incompressible Euler or Navier-Stokes equations is proven. In the mean time, long-time existence for large amplitude smooth solutions of Euler-Poisson system in torus T-d, d greater than or equal to 1, with or without viscosity as the Debye length lambda-->0 is also obtained provided that the smooth solution of incompressible Euler or Navier-Stokes equations exists globally for nearby initial data. In particular, the existence of large amplitude smooth solutions of Euler-Poisson system in torus T-2 with or without viscosity and with sufficiently small Debye length is obtained on any arbitrary time interval. The proof of these results is based on a straightforward extension of the classical energy method, the modulated energy method, the iteration techniques and the standard compactness argument.