and Majda [@Ma1984] (cf. [@Da2010]).

In the multi-dimensional setting, Sideris in [@Si1997] demonstrated using a virial type argument the existence of solutions that form singularities in finite time. The method of proof does not however lead to a classification of the type of singularity produced. The first proof of shock formation in the multi-dimensional setting was given by Christodoulou [@Ch2007], whereby he proved shock formation in the irrotational, relativistic setting. The work was later generalized to non-relativistic, irrotational setting [@ChMi2014], and then further extended by Luk and Speck to the 2D setting with non-trivial vorticity [@LuSp2018]. It is important to note that while the cited work are capable of proving shock formation (or simply singularity formation in the case of Sideris), the methods of proof are incapable of distinguishing precise information on the shock’s profile. For example, none of the cited work determine whether the shock occurs at one specific location or whether multiple shocks occur simultaneously. In the recent work by the first author, Shkoller and Vicol [@BuShVi2019], it was shown than in 2D under the azimuthal symmetry one can prove the existence of stable shocks (stable with respect to perturbations that preserve the azimuthal symmetry) whose self-similar profile 