Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics

In dimension n=2 and 3, we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions isentropic Euler system whenever 1<γ⩽1+2n. This result can be regarded as compressible counterpart one obtained by Székelyhidi–Wiedemann (ARMA, 2012) incompressible flows. Similarly result, admissibility condition is defined in its integral form. Our based on generalization key step convex integration procedure. allows, even case, integrate smooth positive Reynolds stress. A large family subsolutions then considered. These generated, instance, via regularization inviscid limit an associated Navier–Stokes with degenerate viscosities.