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Modulation approximation for the quantum Euler-Poisson equation. (English) Zbl 1476.35228

In this paper, the authors consider the bi-polar Euler-Poisson equations with quantum effect. The main issue of the paper is to consider the modulation approximation for the Euler-Poisson equations, which is a kind of nonlinear Schrödinger equation. The authors make a rigorous justification of such an approximation by taking a modified energy functional and a space-time resonance method.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q40 PDEs in connection with quantum mechanics
35Q35 PDEs in connection with fluid mechanics
35M10 PDEs of mixed type
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
81V74 Fermionic systems in quantum theory
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