# American Institute of Mathematical Sciences

June  2017, 37(6): 3183-3210. doi: 10.3934/dcds.2017136

## Existence of the solution for the viscous bipolar quantum hydrodynamic model

 1 Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing 100088, China 2 Graduate School of China Academy of Engineering Physics, Beijing 100088, China

* Corresponding author: Guangwu Wang

Received  August 2015 Revised  January 2017 Published  February 2017

Fund Project: The first author is supported by National Natural Science Foundation of China-NSAF No.11271052.

In this paper, we investigate the existence of classical solution of the viscous bipolar quantum hydrodynamic(QHD) models for ir-rotational fluid in a periodic domain. By applying the iteration method, we prove that the viscous bipolar QHD model has a local classical solution. Then we prove this solution is global with small initial data, based on a series of a priori estimates. Finally, we obtained the inviscid limit of this viscous quantum hydrodynamic model.

Citation: Boling Guo, Guangwu Wang. Existence of the solution for the viscous bipolar quantum hydrodynamic model. Discrete & Continuous Dynamical Systems, 2017, 37 (6) : 3183-3210. doi: 10.3934/dcds.2017136
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