Stability of Wave Patterns to the Inflow Problem of Full Compressible Navier–Stokes Equations

The inflow problem of full compressible Navier–Stokes equations is considered on the half-line (0,+∞). First, we give the existence (or nonexistence) of the boundary layer solution to the inflow problem when the right end state (ρ₊,u₊,θ₊) belongs to the subsonic, transonic, and supersonic regions, respectively. Then the asymptotic stability of not only the single contact wave but also the superposition of the subsonic boundary layer solution, the contact wave, and the rarefaction wave to the inflow problem are investigated under some smallness conditions. Note that the amplitude of the rarefaction wave is not necessarily small. The proofs are given by the elementary energy method.