论文标题
非线性粘度的量子流体动力学的弱色散冲击曲线的光谱稳定性
Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity
论文作者
论文摘要
本文研究了一个空间维度，在一个空间维度中，由于BOHM电位而具有非线性粘度和分散效应（量子）效应的量子流体动力学系统的弱色散冲击曲线的稳定性。结果表明，如果冲击幅度足够小，则轮廓在光谱上是稳定的。该分析结果与频谱位置的数值估计（Lattanzio，Zhelyazov，Math。模型方法应用Appl。Sci。31，2021）一致。该证明基于光谱水平的能量估计，基于涉及分散势和非线性粘度的扰动的适当加权能函数，以及小型振幅方案中分散曲线的蒙顿性。
This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effects due to a Bohm potential. It is shown that, if the shock amplitude is sufficiently small, then the profiles are spectrally stable. This analytical result is consistent with numerical estimations of the location of the spectrum (Lattanzio, Zhelyazov, Math. Models Methods Appl. Sci. 31, 2021). The proof is based on energy estimates at the spectral level, on the choice of an appropriate weighted energy function for the perturbations involving both the dispersive potential and the nonlinear viscosity, and on the montonicity of the dispersive profiles in the small-amplitude regime.
