Quasineutral Limit of Euler-Poisson System with and without Viscosity
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS Vol. 29, Nos. 3 & 4, pp. 419-456, 2004，-0001，（）：
The quasineutral limit of Euler-Poisson system with and without viscosity in plasma physics in the torusΤd, d ≥ 1 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 Τd, d ≥ 1, with or without viscosity as the Debye length λ→ 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 Τ2 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.
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