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

Abstract

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^{+}=(0,+\infty )$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 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 degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.

27 pages

Cited by in corpus (5)

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• Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
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• Large-time behavior of solutions to the outflow problem for the compressible Navier-Stokes-Maxwell equations
• Stability of degenerate stationary solution to the outflow problem for full Navier-Stokes equations