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

Gui-Qiang Chen, Mikhail Feldman, Jingchen Hu, Wei Xiang

Published 2017-05-19Version 1

We are concerned with the regularity of solutions of the Lighthill problem for shock diffraction by a convex corned wedge. 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.