Gradient blowup without shock formation in compressible Euler flow

The well-known Guderley similarity solution provides a fundamental example of how a spherically converging shock wave can generate amplitude blowup in compressible Euler flow. Recent work has shown that the same phenomenon can occur in continuous flow. In this work, we analyze a different type of continuous similarity flows in which density, velocity, and sound speed all suffer gradient blowup at collapse, while remaining locally bounded. We give examples where, notwithstanding the presence of gradient singularities, no shock wave appears at collapse and the flow is globally continuous.