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Quasineutral limit of Euler-Poisson system with and without viscosity. (English) Zbl 1140.35551

The author examines the title problem from plasma physics in the torus \(\mathbb T^d\), \(d>1\), and proves the long-time existence for large-amplitude smooth solutions as the Debye length tends to \(0\), provided that smooth solutions of incompressible Euler or Navier-Stokes equations exist globally for nearby initial data. The proof is based on an energy estimate in weighted Sobolev spaces, the modulated energy method, iteration techniques and standard compactness arguments. The author claims that the developed method can be applied to establish the asymptotic limit of the quantum hydrodynamic Euler-Poisson system and to study the viscosity-vanishing limit of Navier-Stokes equations.

MSC:

35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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