| Abstract: |
| In dimension 2 or 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 to the isentropic Euler system. This result can be regarded as a compressible counterpart of the one obtained by Szekelyhidi-Wiedemann (ARMA, 2012) for incompressible flows. Similarly to the incompressible result, the admissibility condition is defined in its integral form. Our result is based on a generalization of a key step of the convex integration procedure. This generalization allows, even in the compressible case, to convex integrate any smooth positive Reynolds stress. A large family of subsolutions can then be considered. These subsolutions can be generated, for instance, via regularization of any weak inviscid limit of an associated compressible Navier-Stokes system with degenerate viscosities. |
|