# American Institute of Mathematical Sciences

January  2017, 16(1): 273-294. doi: 10.3934/cpaa.2017013

## Quasineutral limit for the quantum Navier-Stokes-Poisson equations

 1 School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 2 Department of Mathematics, Chongqing University, Chongqing 401331, China 3 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Received  May 2016 Revised  September 2016 Published  September 2016

Fund Project: The second author is supported by NSFC (grant 11471057) and the Fundamental Research Funds for the Central Universities (grant Project No. 106112016CDJZR105501). The third author is supported by NSFC (grant 11371042) and the key fundation of Beijing Municipal Education Commission.

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 $\hbar>0$.

Citation: Min Li, Xueke Pu, Shu Wang. Quasineutral limit for the quantum Navier-Stokes-Poisson equations. Communications on Pure & Applied Analysis, 2017, 16 (1) : 273-294. doi: 10.3934/cpaa.2017013
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