论文标题
从量子 - 纳维尔 - stokes方程到量子漂移扩散方程的松弛极限
Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation
论文作者
论文摘要
从有限能量弱解决方案的框架中执行了量子 - 奈维尔 - 散景系统到量子漂移扩散方程的松弛时间极限。没有对限制解决方案的假设。证明利用了通过能量和BD熵估计来推断的适当缩放的先验范围。此外，从这些估计中显示了如何在限制下回收与扩散进化相关的自由能估计值。作为副产品，我们的主要结果还为存在有限的能量弱解决方案提供了量子漂移扩散方程的替代证明。
The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to the quantum drift-diffusion equation is performed in the framework of finite energy weak solutions. No assumptions on the limiting solution are made. The proof exploits the suitably scaled a priori bounds inferred by the energy and BD entropy estimates. Moreover, it is shown how from those estimates the Fisher entropy and free energy estimates associated to the diffusive evolution are recovered in the limit. As a byproduct, our main result also provides an alternative proof for the existence of finite energy weak solutions to the quantum drift-diffusion equation.
