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We consider a class of "wild" initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural L 1 -topology and show that its complement is rather large, specifically it is an open dense set. Mathematics Subject Classificationdoi:10.1007/s00526-020-01806-5 fatcat:e45kphphwjhofbjv6iq6t3qftq