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Using the method developed by Camillo De Lellis and Laszlo Szekelyhidi for the incompressible Euler system we prove that in the case of compressible isentropic Euler equations it holds that for every Riemann initial data such that the corresponding self-similar solution consists of 2 shocks there exists also infinitely many other admissible weak solutions.Moreover,for some of these initial data the self-similar solution is not "entropy rate admissible" in the sense of Dafermos.