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We consider a particular instance of reflection of shock waves inself-similar compressible flow. We prove that local self-similar regularreflection (RR) cannot always be extended into a global flow. Therefore thedetachment criterion is not universally correct. More precisely, consider thefollowing "angle condition": the tangent of the strong-type reflected shockmeets the opposite wall at a sharp or right downstream side angle. In caseswhere the condition is violated and the weak-type reflected shock is transonic,we show that global RR does not exist. Combined with earlier work we have shownthat none of the classical criteria for RR-MR transition is universallycorrect. A new criterion is proposed. Moreover, we have shown that strong-typeRR is unstable, in the sense that global RR cannot persist under perturbationsto one side. This yields a definite answer to the weak-strong problem becauseearlier work shows stability of weak RR in the same sense.

Instability of Strong Regular Reflection and Counterexamples to the Detachment Criterion