LOSS OF REGULARITY OF SOLUTIONS OF THE LIGHTHILL PROBLEM FOR SHOCK DIFFRACTION FOR POTENTIAL FLOW

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

6 Scopus Citations
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Author(s)

  • Gui-Qiang CHEN
  • Mikhail FELDMAN
  • Jingchen HU
  • Wei XIANG

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1096-1114
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume52
Issue number2
Online published12 Mar 2020
Publication statusPublished - 2020

Abstract

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 achievethe nonexistence 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.

Research Area(s)

  • Compressible flow, Conservation laws, Degenerate elliptic equations, Free boundary problems, Lighthill problem, Loss of regularity, Mixed elliptic-hyperbolic type, Nonlinear equations of second order, Potential flow equation, Shock diffraction

Citation Format(s)

LOSS OF REGULARITY OF SOLUTIONS OF THE LIGHTHILL PROBLEM FOR SHOCK DIFFRACTION FOR POTENTIAL FLOW. / CHEN, Gui-Qiang; FELDMAN, Mikhail; HU, Jingchen et al.

In: SIAM Journal on Mathematical Analysis, Vol. 52, No. 2, 2020, p. 1096-1114.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review