Non-existence of strong regular reflections in self-similar potential flow

TL;DR

This paper proves that in self-similar potential flow, strong regular shock reflections do not exist within a natural class of solutions, ensuring the well-posedness of the problem by excluding these non-physical solutions.

Contribution

It establishes the non-existence of global strong-shock solutions in self-similar potential flow, clarifying the uniqueness and stability of weak shock solutions.

Findings

Strong-shock solutions do not exist in the considered class.

Ensures well-posedness of potential flow shock reflection problems.

Supports the physical relevance of weak shock solutions.

Abstract

We consider shock reflection which has a well-known local non-uniqueness: the reflected shock can be either of two choices, called weak and strong. We consider cases where existence of a global solution with weak reflected shock has been proven, for compressible potential flow. If there was a global strong-shock solution as well, then potential flow would be ill-posed. However, we prove non-existence of strong-shock analogues in a natural class of candidates.