  Radial similarity flow offers a rare instance where concrete inviscid,
multi-dimensional, compressible flows can be studied in detail. In particular,
there are flows of this type that exhibit imploding shocks and cavities. In
such flows the primary flow variables (density, velocity, pressure,
temperature) become unbounded at time of collapse. In both cases the solution
can be propagated beyond collapse by having an expanding shock wave reflect off
the center of motion.
  These types of flows are of relevance in bomb-making and inertial confinement
fusion, and also as benchmarks for computational codes; they have been
investigated extensively in the applied literature. However, despite their
obvious theoretical interest as examples of unbounded solutions to the
multi-dimensional Euler system, the existing literature does not address to
what extent such solutions are bona fide weak solutions.
  In this work we review the construction of globally defined radial similarity
shock and cavity flows, and give a detailed description of their behavior
following collapse. We then prove that similarity shock solutions provide
genuine weak solutions, of unbounded amplitude, to the multi-dimensional Euler
system. However, both types of similarity flows involve regions of vanishing
pressure prior to collapse (due to vanishing temperature and vacuum,
respectively) - raising the possibility that Euler flows may remain bounded in
the absence of such regions.
