  We are concerned with the suitability of the main models of compressible
fluid dynamics for the Lighthill problem for shock diffraction by a convex
corned wedge, by studying the regularity of solutions of the problem, which can
be formulated as a free boundary problem. In this paper, we prove that there is
no 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 least
a characteristic discontinuity (vortex sheet or entropy wave) is expected to be
generated, which is consistent with the experimental and computational results.
Therefore, the potential flow equation is not suitable for the Lighthill
problem so that the compressible Euler system must be considered. In order to
achieve the non-existence result, a weak maximum principle for the solution is
established, and several other mathematical techniques are developed. The
methods and techniques developed here are also useful to the other problems
with similar difficulties.
