Diffusive wave in the low Mach number limit for the compressible Navier–Stokes–Korteweg equations with general initial data

This paper investigates the low Mach number limit for the non-isentropic compressible Navier–Stokes–Korteweg equations with general initial data in one dimension, in which the density and temperature have different asymptotic states at the far field. The result shows that the verification of the limit relies on the uniform estimates including weighted time derivatives. In particular, the temperature difference between the far-field states is allowed to be arbitrarily large in this paper.