论文标题
量子流体动力学中小振幅色散冲击的光谱稳定性粘度
Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity
论文作者
论文摘要
在一个空间维度中，在量子流体动力学的背景下，在一个空间维度中可压缩的粘性欧拉系统。色散项是由于通过BOHM电位描述的量子效应引起的，粘度项为线性类型。结果表明，所考虑的系统的小振幅粘性分散性休克轮廓在光谱上是稳定的，以这种方式证明了Lattanzio等人先前的数值观察。 （Phys。D402，2020，p。132222; Appl。Math。Comput。385，2020，p。125450）。该证明是基于光谱能量估计，哪些在小型振幅方面的单调性中获利。
A compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The dispersive term is due to quantum effects described through the Bohm potential and the viscosity term is of linear type. It is shown that small-amplitude viscous-dispersive shock profiles for the system under consideration are spectrally stable, proving in this fashion a previous numerical observation by Lattanzio et al. (Phys. D 402, 2020, p. 132222; Appl. Math. Comput. 385, 2020, p. 125450). The proof is based on spectral energy estimates which profit from the monotonicty of the profiles in the small-amplitude regime.
