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

2009/03/24 by Xiaohong Qin, Yi Wang, Qin, Xiaohong +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AG #math.AP

paper · pdf · doi:10.48550/arxiv.0903.4004

34 pages

arxiv created 2009/03/25 · arxiv updated 2009/12/01

Abstract

The inflow problem of full compressible Navier-Stokes equations is considered on the half line (0,+∞). Firstly, we give the existence (or non-existence) 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 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 can be arbitrarily large. The proofs are given by the elementary energy method.

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• Stability of viscous shock for the Navier-Stokes-Fourier system: outflow and impermeable wall problems

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