  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--Sz\'ekelyhidi, 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
$\Lambda$-convex hull of the constitutive set. An important application of our
scheme will be exhibited in forthcoming work by Gallenm\"uller--Wiedemann.
