论文标题
依赖密度粘度的Korteweg流体的高马赫数限制
High Mach number limit for Korteweg fluids with density dependent viscosity
论文作者
论文摘要
本文的目的是研究具有密度依赖性粘度的Korteweg类型的可压缩压缩流体的高马赫数流动。特别是我们考虑等温毛细管和量子可压缩流体的模型。对于毛细管案例，我们证明了系统的弱解决方案和相关特性，而无需压力，以及在高马赫数限制中的溶液的收敛性。在量子案例中，也证明了后者的，该量子在该量子的框架中还讨论了该系统的“增强”版本的框架。此外，作为我们结果的副产品，如果毛细血管流体具有特殊选择的初始速度基准，我们获得了有关真空区域传播的有趣属性。
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.
