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

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.