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We consider the complete Euler system describing the time evolution of aninviscid non-isothermal gas. We show that the rarefaction wave solutions of the1D Riemann problem are stable, in particular unique, in the class of allbounded weak solutions to the associated multi-D problem. This may be seen as acounterpart of the non-uniqueness results of physically admissible solutionsemanating from 1D shock waves constructed recently by the method of convexintegration.

Stability of the isentropic Riemann solutions of the full multidimensional Euler system