稳态双极黏滞量子流体力学模型的正解的存在性  

The Existence of Positive Solution of the Steady-state Bipolar Viscous Quantum Hydrodynamic Model

作　　者：毛磊[1] 张燕[1] 寇冰煜[1] 刘凤 

机构地区：[1]解放军理工大学理学院,南京211101 [2]气象学院,南京211101

出　　处：《科学技术与工程》2012年第24期5961-5965,5988,共6页Science Technology and Engineering

摘　　要：研究一类带有特殊黏滞项的稳态双极流体力学模型正解的存在性。这个模型含有三阶量子修正项和二阶黏滞项。先将原方程组变形为常见的形式。得到原问题的等价问题利用先验估计和Leray-Schauder不动点定理。证明了无论是等熵还是等温条件下,对于所有的电流密度,此模型存在正解。The weak solution of the steady-state bipolar quantum hydrodynamic equations with special viscous terms is studied. The model equations contain a third-order quantum correction term and second-order viscous term which are derived from a Wigner-Fokker-Planck model. By using prior estimates and Leray-Schauder fixed point theorem, it is shown that, in the case of isothermal or isentropic, the equations have a positive solution for all current density.

关 键 词：量子流体力学 黏滞 双极 不动点定理 正解 

分 类 号：O345[理学—固体力学]