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

@inproceedings{Barker2019ExistenceAS, title={Existence and stability of steady noncharacteristic solutions on a finite interval of full compressible Navier-Stokes equations}, author={Blake Barker and Benjamin Melinand and Kevin Zumbrun}, year={2019} }

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… CONTINUE READING

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