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arXiv:2501.05134 [math.AP]AbstractReferencesReviewsResources

Regularity and well-posedness of the Euler system in gas dynamics for dissipative solutions

Eduard Feireisl, Ansgar Jüngel, Mária Lukáčová-Medvid'ová

Published 2025-01-09Version 1

We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two step, selection procedure to identify a unique semigroup solution in the class of dissipative solutions to the Euler system. Finally, we introduce a refined version of Dafermos' criterion yielding a unique solution of the problem for any finite energy initial data.

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