量子流体动力学等温模型的拟中性极限

摘要

The isothermal quantum hydrodynamic model in three dimensional space is investigated. The model is one of the quantum macroscopic models used to simulate the quantum effects in miniaturized semiconductor devices, and it reflects the nonlinear relation among the electron density, the electron velocity and the electrostatic potential. The model contains a nonlinear third-order derivative item, which induces mathematical difficulties. By using the energy functional method and the weak convergence compactness method, the smooth solution of the model converges to the strong solution of incompressible Euler equations is proved under periodic boundary conditions.%研究三维量子流体动力学等温模型,它是用来模拟超小半导体器件发生量子效应的宏观量子模型之一,反映了电子浓度、电子速度以及静电场位势之间的非线性关系.该模型中含有非线性三阶导数项,这在数学上给研究该模型带来了困难.在周期边界条件下,利用能量泛函方法和弱收敛紧性方法证明了当德拜长度趋于零时,其光滑解收敛于不可压缩Euler方程的强解.