For the isothermal Euler equations, every bounded-variation entropy solution is unique and L2-stable in the class of weak entropy solutions with strong traces, without any smallness assumption on the variation.
W ave-front tracking for the equations of isentropic gas dynamics
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Uniqueness & Weak-BV Stability in the Large for Isothermal Gas Dynamics
For the isothermal Euler equations, every bounded-variation entropy solution is unique and L2-stable in the class of weak entropy solutions with strong traces, without any smallness assumption on the variation.