Abstract
The global stability of Lipschitz continuous solutions with discontinuous initial data is established in a broad class of entropy solutions in \(L^\infty\) containing vacuum states. In particular, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in \(L^\infty\).
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Li, Y. Global stability of solutions with discontinuous initial data containing vacuum states for the isentropic Euler equations . Z. angew. Math. Phys. 55, 48–62 (2004). https://doi.org/10.1007/s00033-003-3005-8
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DOI: https://doi.org/10.1007/s00033-003-3005-8