Title: Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow,
Abstract: We are concerned with the regularity of solutions of the Lighthill problem
for shock diffraction by a convex corned wedge, 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.
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.