Large-time behavior of solutions to an inflow problem for the compressible Navier-Stokes-Korteweg equations in the half space (Q2084970)

The authors study the one-dimensional compressible Navier-Stokes-Korteweg system for density and velocity of an adiabatic flow. The focus is on the large-time behaviour of solutions to the inflow problem: the boundary data are given at \(x=0\), and the spatial domain is \(x>0\). Another boundary condition is a finite limit at infinity. Existence of the boundary-layer solution is established, and its stability is proved for ``small'' boundary data.