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We are concerned with the suitability of the main models of compressiblefluid dynamics for the Lighthill problem for shock diffraction by a convexcorned wedge, by studying the regularity of solutions of the problem, which canbe formulated as a free boundary problem. In this paper, we prove that there isno regular solution that is subsonic up to the wedge corner for potential flow.This indicates that, if the solution is subsonic at the wedge corner, at leasta characteristic discontinuity (vortex sheet or entropy wave) is expected to begenerated, which is consistent with the experimental and computational results.Therefore, the potential flow equation is not suitable for the Lighthillproblem so that the compressible Euler system must be considered. In order toachieve the non-existence result, a weak maximum principle for the solution isestablished, and several other mathematical techniques are developed. Themethods and techniques developed here are also useful to the other problemswith similar difficulties.

Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow