High Mach number limit for Korteweg fluids with density dependent viscosity

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates high Mach number flows for compressible barotropic fluids of Korteweg type with density dependent viscosity. The existence of weak solutions and the convergence of solutions in the high Mach number limit are proven. Additionally, an interesting property concerning the propagation of vacuum zones is obtained for a capillary fluid with a specific choice of initial velocity datum.