In this talk, we will present our recent results for the boundary value problem of steady compressible Navier-Stokes equations. A new type of slip boundary conditions has been systematically derived by Kazuo Aoki and his collaborators in 2017 and 2018. These boundary conditions naturally appear in the slip-flow theory, with the aim to reproduce the correct overall solutions of the corresponding boundary value problem of the Boltzmann equation for small Knudsen numbers. Thus a natural question is that whether the boundary value problem for the hydrodynamic system under the new slip boundary conditions is well-posed in the Hadamard’s sense. Here, we give an affirmative answer to the question.