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Some asymptotic analysis in steady-state Euler-Poisson equations for potential flow. (English) Zbl 1051.82026

The hydrodynamic model is used to describe the plasma behaviour in mathematical modelling and numerical simulation of plasmas. The problem envisaged is the coupled equation of continuity and Euler equation. It is shown that there is a unique solution when the electron-mass is small enough. For zero-electron-mass limit and zero-relaxation-time limit the sequence of solutions is proven to converge, and the corresponding error estimates are given. For the case of quasi-neutral limit, however, similar results are obtained only in the case if the given boundary data are in equilibrium.

MSC:

82D10 Statistical mechanics of plasmas
35Q35 PDEs in connection with fluid mechanics
82D37 Statistical mechanics of semiconductors
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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