Time of first blowup for the 3D relativistic Euler equations with vorticity and entropy

Let the simple isentropic plane-symmetric solutions of Theorem 1D singular boundary and crease be background solutions to the 3D relativistic Euler equations with symmetry. Consider smooth initial data in 3D, without assumptions of symmetry, irrotationality, or isentropicity, that are close in a sufficiently high-order Sobolev space to the data of one of the background solutions. Let $T_{\mathrm{Shock}}$ denote the shock-formation time of the background solution, and let $\partial_-\mathcal{B}$ denote the crease in the conjectured maximal globally hyperbolic development.

Time-of-first-blowup conjecture. The perturbed solution forms a shock at a time that is a perturbation of $T_{\mathrm{Shock}}$; its first blowup time is the smallest value of $t$ along the crease $\partial_-\mathcal{B}$.

This conjecture concerns the stability of shock formation for general small, non-symmetric perturbations of simple isentropic plane-symmetric solutions, including perturbations with vorticity and entropy. The corresponding local picture has been justified for open sets of initial data for the 3D compressible Euler equations, but the relativistic assertion remains open.