Large-time behavior of smooth solutions to the isothermal compressible fluid models of Korteweg type with large initial data (Q739438)

In this article the author considers the large-time behavior of smooth solutions of the Cauchy problem for the 1D barotropic compressible Navier-Stokes-Korteweg system with density dependent viscosities. Depending whether the far-field of the data are the same when \(x\to\pm\infty\) or not, he proves that the problem admits a unique global smooth solution tending either to a constant state, or a rarefaction wave for large times.