Non-uniqueness of admissible weak solutions to the two-dimensional barotropic compressible Euler system with contact discontinuities

This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak solutions is established for certain Riemann initial data for which the corresponding one-dimensional self-similar solution consists solely of a contact discontinuity.