论文标题
分析描述量子流体的一类流体动力系统的声学振荡
Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids
论文作者
论文摘要
量子流体的流体动力系统是用于可压缩流体流的系统，量子效应在宏观上相关。我们讨论描述量子效应的色散张量的存在如何改变量子流体动力系统（QHD）的示例的声学分散体。对于QHD系统，分散关系由Bogoliubov色散关系给出，用于弱相互作用的玻璃气体。我们提供精致的Strichartz估计值，允许精确控制声学振荡。讨论了量子Navier-Stokes方程和QHD系统的低马赫数限制的应用。分散分析概括了一些用于毛细血管流体的Euler和Navier-Stokes-Korteweg系统。
Hydrodynamic systems for quantum fluids are systems for compressible fluid flows for which quantum effects are macroscopically relevant. We discuss how the presence of the dispersive tensor describing the quantum effects alters the acoustic dispersion at the example of the Quantum Hydrodynamic system (QHD). For the QHD system the dispersion relation is given by the Bogoliubov dispersion relation for weakly interacting Bose gases. We provide refined Strichartz estimates allowing for an accurate control of acoustic oscillations. Applications to the low Mach number limit for the quantum Navier-Stokes equations and the QHD system are discussed. The dispersive analysis generalizes to some Euler- and Navier-Stokes-Korteweg systems for capillary fluids.
