The full viscous quantum hydrodynamic system in one dimensional space
The full viscous quantum hydrodynamic system in one dimensional space
复制标题
一维空间全粘性量子流体动力系统
DOI：
10.1063/5.0125284
复制
发表时间：
2023
影响因子：
1.3
通讯作者：
Xiaoying Han
中科院分区：
文献类型：
--
作者：
Wenlong Sun;Yeping Li;Xiaoying Han
在空间一维真实的直线上研究了粒子密度、电流密度、能量密度和静电势与Poisson方程耦合的粘性量子流体动力学系统。该系统是自洽的，在这个意义上的电场，形成一个强迫项的动量和能量方程，是由耦合泊松方程。首先，在适当的Sobolev空间中证明了平稳解的存在唯一性。然后，指数稳定的平稳解建立通过构造一个先验估计。由于经典流体动力学方程的技术不适用于这里由于量子项，局部时间解的存在性是通过显示局部时间解的存在性的一个重新制定的系统通过迭代方法获得。
A viscous quantum hydrodynamic system for particle density, current density, energy density, and electrostatic potential, coupled with a Poisson equation, is studied in spatial one dimensional real line. The system is self-consistent in the sense that the electric field, which forms a forcing term in the momentum and energy equations, is determined by the coupled Poisson equation. First, the existence and uniqueness of the stationary solution is proved in an appropriate Sobolev space. Then, exponential stability of the stationary solution is established by constructing an a priori estimate. Since the techniques for classical hydrodynamic equations are not applicable here due to the quantum term, the existence of a local-in-time solution is obtained by showing the existence of local-in-time solutions of a reformulated system via the iteration method.