Stability of a one-dimensional full viscous quantum hydrodynamic system
Analysis of PDEs
2023-07-03 v1 Dynamical Systems
Abstract
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and uniqueness of a steady-state solution to the quantum hydrodynamic system is established. Then, utilizing the fact that the third order perturbation term has an appropriate sign, the local-in-time existence of the solution is investigated by introducing a fourth order viscous regularization and using the entropy dissipation method. In the end, the exponential stability of the steady-state solution is shown by constructing a uniform a-priori estimate.
Cite
@article{arxiv.2306.17495,
title = {Stability of a one-dimensional full viscous quantum hydrodynamic system},
author = {Xiaoying Han and Yuming Qin and Wenlong Sun},
journal= {arXiv preprint arXiv:2306.17495},
year = {2023}
}