The aim of this paper is to investigate the regime of high Mach number flows for compressible barotropic fluids of Korteweg type with density dependent viscosity. In particular we consider the models for isothermal capillary and quantum compressible fluids. For the capillary case we prove the existence of weak solutions and related properties for the system without pressure, and the convergence of the solution in the high Mach number limit. This latter is proved also in the quantum case for which a weak-strong uniqueness analysis is also discussed in the framework of the so-called “augmented” version of the system. Moreover, as byproduct of our results, in the case of a capillary fluid with a special choice of the initial velocity datum, we obtain an interesting property concerning the propagation of vacuum zones.

本文的目的是研究具有密度依赖性粘度的Korteweg型可压缩正压流体的高马赫数流态。特别是，我们考虑了等温毛细管和量子可压缩流体的模型。对于毛细管情况，我们证明了在无压力的情况下系统存在弱解和相关性质，并且在高马赫数极限下解的收敛性。后一种情况在量子情况下也得到了证明，在这种情况下，在系统的“增强”版本的框架中还讨论了弱强唯一性分析。此外，作为我们结果的副产品，在毛细管流体具有特殊选择的初始速度数据的情况下，我们获得了有关真空区域传播的有趣特性。