Small isothermal Euler shocks are stable and unique in the class of vanishing viscosity limits, even under large perturbations of finite relative entropy.
Uniqueness & Weak-BV Stability in the Large for Isothermal Gas Dynamics
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abstract
For the $1$-d isothermal Euler system, we consider the family of entropic BV solutions with possibly large, but finite, total variation. We show that these solutions are stable with respect to large perturbations in a class of weak solutions to the system which may not even be BV. The method is based on the construction of a modified front tracking algorithm, in which the theory of $a$-contraction with shifts for shocks is used as a building block. The main contribution is to construct the weight in the modified front tracking algorithm in a large-BV setting.
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Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows
Small isothermal Euler shocks are stable and unique in the class of vanishing viscosity limits, even under large perturbations of finite relative entropy.