Wild non-uniqueness conjecture for two-dimensional isentropic Euler Riemann problems

Let $(\rho_-,v_{-1},v_{-2})$ and $(\rho_+,v_{+1},v_{+2})$ be any Riemann initial data for the two-dimensional isentropic Euler system, and let $p$ be a smooth pressure law satisfying $p'>0$. A bounded solution is admissible if it satisfies the system and the admissibility condition specified in the paper.

Wild non-uniqueness conjecture. For any such Riemann initial data, there exists a smooth pressure law $p$ with $p'>0$ such that the corresponding system admits infinitely many bounded, admissible solutions with those Riemann initial data.

The conjecture proposes that the non-uniqueness produced by convex integration is not restricted to the particular contact discontinuity studied in the paper, but can occur for arbitrary Riemann data after choosing a suitable pressure law. The computational experiments reported in the paper support this expectation, but do not establish it.