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

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.