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<p>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.</p>

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Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月3日

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  • Eduard Feireisl,
  • Ansgar Jüngel,
  • Mária Lukáčová-MedviĎová

摘要

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.