Large-Time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier–Stokes equations is investigated on the half line $\mathbf{R}_+=(0,+\infty)$. The wave structure, which contains four waves—the transonic (or degenerate) boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave, and the 3-rarefaction wave to the inflow problem—is described, and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier–Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the treatments of the degeneracies in the transonic boundary layer solution and the wave interactions in the superposition wave.

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