Stationary solutions to the one-dimensional full compressible Navier-Stokes-Korteweg equations in the half line

This paper is concerned with the stationary solutions to the one-dimensional full (non-isentropic) compressible Navier-Stokes-Korteweg equations with far field states and boundary data in the half line. When the fluids enter into and blow out the region through the boundary, respectively, the unique existence of the stationary solutions to the one-dimensional full compressible Navier-Stokes-Korteweg equations in the half line is shown provided that the boundary strength is small enough. Moreover, we also give the spatial decay rates of the stationary solutions. The main ingredient of the proof is the manifold theory and the center manifold theorem that take the accurate analysis of the cubic characteristic equations. (c) 2023 Elsevier Inc. All rights reserved.