Global smooth solutions of 3‐D Navier‐Stokes‐Korteweg equations with large initial data

Abstract

In this paper, we consider the Cauchy problem to the tri‐dimensional compressible Navier‐Stokes‐Korteweg system with a specific choice on the Korteweg tensor in the whole space and establish the global solutions to the tri‐dimensional Navier‐Stokes‐Korteweg equations with a class of large initial data whose L2 norm can be arbitrarily large.