Constant Cutoffs to Self-Similar Implosions for Compressible Euler

Implosions for the Compressible Euler equations are an example of finite time blowup in hyperbolic conservation laws. Much recent development extends the work of Guderley to construct smooth, self-similar implosions in the isentropic setting. However, these solutions are very numerically unstable. Another smooth, self-similar solution is the Kidder solution which is explicit and numerically stable, but radially unbounded.

We consider constant cutoffs to the Kidder initial data as a way of remediating the radial unboundedness. In 1D, a rarefaction emerges and subsumes the implosion. In higher dimensions, the implosion persists.

This work is done in conjunction with Los Alamos National Laboratory.