论文标题
非线性粘度的量子流体动力学的行进波
Traveling waves for quantum hydrodynamics with nonlinear viscosity
论文作者
论文摘要
在本文中，我们研究了具有分散体（通过BOHM电位对量子效应建模量子效应）和非线性粘度在量子流体动力模型的背景下的量子效应（通过BOHM电位模拟量子效应）的流动波的存在。证明了剖面的存在，用于适当的（超级或子语音）终端状态，这些状态定义了基础欧拉系统以密度和速度形式的基础欧拉系统的震动，而无需限制粘度和分散参数。另一方面，分散和粘度的相互作用在证明振荡概况的存在中起着至关重要的作用，以这种方式显示了色散如何在某些制度中起重要作用。还提供了数值实验来分析此类曲线相对于粘度/分散项的灵敏度以及与真空的近乎近似。
In this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in the context of quantum hydrodynamic models for superfluidity. The existence of profiles is proved for appropriate (super- or sub- sonic) end states defining Lax shocks for the underlying Euler system formulated in terms of density and velocity without restrictions for the viscosity and dispersion parameters. On the other hand, the interplay of the dispersion and the viscosity plays a crucial role in proving the existence of oscillatory profiles, showing in this way how the dispersion plays a significant role in certain regimes. Numerical experiments are also provided to analyze the sensitivity of such profiles with respect to the viscosity/dispersion terms and with respect to the nearness to vacuum.
