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Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics
Eduard Feireisl1,2, Ansgar Jüngel3,2, Mária Lukáčová-Medvid'ová4,2
1Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic.
Abstract:
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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