A general convex integration scheme for the isentropic compressible Euler equations

We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least 2) to exact weak solutions. The method is closely related to the incompressible scheme established by De Lellis–Székelyhidi, in particular, we only perturb momenta and not densities. Surprisingly, though, this turns out not to be a restriction, as can be seen from our simple characterization of the [Formula: see text]-convex hull of the constitutive set. An important application of our scheme has been exhibited in recent work by Gallenmüller–Wiedemann.