Small isothermal Euler shocks are stable and unique in the class of vanishing viscosity limits, even under large perturbations of finite relative entropy.
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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.