In this paper, we consider the problem with a gas–gas free boundary for the one dimensional isentropic compressible Navier–Stokes–Korteweg system. For shock wave, asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary, and prove that if the initial data around the shifted viscous shock profile and its strength are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. Also, we show the asymptotic stability toward rarefaction wave without the smallness on the strength if the initial data around the rarefaction wave are sufficiently small.

在本文中，我们考虑了一维等熵可压缩Navier–Stokes–Korteweg系统的无气边界问题。对于冲击波，问题的渐近曲线显示为已移动的粘性冲击曲线，它适当地远离边界，并证明如果在已移动的粘性冲击曲线周围的初始数据及其强度足够小，则该问题拥有独特的全球性强解决方案，随着时间的流逝，粘滞冲击曲线趋于变化。另外，如果围绕稀疏波的初始数据足够小，我们将显示出对稀疏波的渐近稳定性，而强度不会减小。