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arXiv · 1510.03960

Quasineutral limit for the quantum Navier-Stokes-Poisson equation

Min Li·Xueke Pu·Shu Wang
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Abstract

In this paper, we study the quasineutral limit and asymptotic behaviors for the quantum Navier-Stokes-Possion equation. We apply a formal expansion according to Debye length and derive the neutral incompressible Navier-Stokes equation. To establish this limit mathematically rigorously, we derive uniform (in Debye length) estimates for the remainders, for well-prepared initial data. It is demonstrated that the quantum effect do play important roles in the estimates and the norm introduced depends on the Planck constant $\hbar>0$.

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Min Li, Xueke Pu, Shu Wang. 2016-08-22. Quasineutral limit for the quantum Navier-Stokes-Poisson equation. https://arxiv.org/abs/1510.03960

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