High Mach number limit for Korteweg fluids with density dependent viscosity

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