Existence and stability of steady noncharacteristic solutions on a finite interval of full compressible Navier-Stokes equations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2019

Existence and stability of steady noncharacteristic solutions on a finite interval of full compressible Navier-Stokes equations

Blake Barker
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Kevin Zumbrun
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Abstract

We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present also numerical experiments indicating uniqueness and time-asymptotic stability of such solutions. At the same time, we give an example of an (artificial) equation of state possessing a convex entropy for which there holds nonuniqueness of solutions. This is associated with instability and Hopf bifurcation to time-periodic solutions.
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Dates and versions

hal-02352676 , version 1 (12-11-2019)
hal-02352676 , version 2 (23-03-2020)
hal-02352676 , version 3 (12-04-2023)

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Blake Barker, Benjamin Melinand, Kevin Zumbrun. Existence and stability of steady noncharacteristic solutions on a finite interval of full compressible Navier-Stokes equations. 2019. ⟨hal-02352676v1⟩
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