一维等温量子Navier-Stokes方程组的热平衡状态

Thermal Equilibrium State of the Isothermal Quantum Navier-Stokes Equations in One Dimension

研究发生在半导体器件中的一种耗散的量子流体动力学模型,即一维等温量子Navier-Stokes方程组.在热平衡状态下,先利用指数变换法将问题转化成一个四阶椭圆方程,然后利用Leray-Schauder不动点定理得到了模型古典解的存在性,最后在某些条件下证明了解的唯一性.

A dissipative quantum hydrodynamic model arising in semiconductor device,i.e.one-dimensional isothermal quantum Navier-Stokes equations is studied.The problem is reformulated as a fourth-order elliptic equation by using an exponential variable transformation in thermal equilibrium state.Then the existence of the classical solution to the model is obtained using the LeraySchauder fixed-point theorem.Finally,the uniqueness of the solution is proved under some conditions.