Low Mach number limit of the full compressible Navier-Stokes-Korteweg equations with general initial data

In this paper, the low Mach number limit for the three-dimensional full compressible Navier-Stokes-Korteweg equations with general initial data is rigorously justified within the framework of local smooth solution.Under the assumption of large temperature variations, we first obtain the uniform-in-Mach-number estimates of the solutions in a ε-weighted Sobolev space, which establishes the local existence theorem of the three-dimensional full compressible Navier-Stokes-Korteweg equations on a finite time interval independent of Mach number.Then, the low mach limit is proved by combining the uniform estimates and a strong convergence theorem of the solution for the acoustic wave equations.This result improves that of [K.-