can be precisely described. This work in [@BuShVi2019b] was extended to 3D in the absence of any symmetry assumption, and further extended to the non-isentropic case in [@BuShVi2019c]. In a different direction, we would like to also bring to attention of the remarkable recent works of Merle, Raphael, Rodnianski, and Szeftel, [@MRRS1], [@MRRS2], which demonstrated the existence of radially symmetric imploding solutions to the isentropic Euler equation – a completely new form of singularity for the Euler equations.

Unstable shocks for the Burgers’ equation {#s:burgers}
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Before we state a rough version of the main theorem, let us first review the concept of an *unstable shock* in the context of the 1D Burgers’ equation: $$\label{eq:Burgers}
{\ensuremath{\partial}}_t w+ w {\ensuremath{\partial}}_y w = 0\,\quad\mbox{for }y\in\mathbb R\,.$$ The Burgers’ equation satisfies the following four invariances:

1.  Galilean symmetry: If $w(y,t)$ is solves then $w(y-v,t)+v$ solves for any $v\in\mathbb R$.

2.  Temporal rescaling: If $w(y,t)$ is solves then $\lambda w(y,\lambda t)$ solves for any $\lambda>0$.

3.  Translation invariance: If $w(y,t)$ is solves then $w(y-y_0, t)$ solves for any $y_0\in\mathbb R$.

4.  Spatial rescaling: If $w(y,t)$ is solves then $\lambda^{-1} w(\lambda y,t)$ solves for any $\lambda>0$.

Any initial data $w_0$ with a negative slope at 