TY - JOUR
T1 - LOSS OF REGULARITY OF SOLUTIONS OF THE LIGHTHILL PROBLEM FOR SHOCK DIFFRACTION FOR POTENTIAL FLOW
AU - CHEN, Gui-Qiang
AU - FELDMAN, Mikhail
AU - HU, Jingchen
AU - XIANG, Wei
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Compressible flow
KW - Conservation laws
KW - Degenerate elliptic equations
KW - Free boundary problems
KW - Lighthill problem
KW - Loss of regularity
KW - Mixed elliptic-hyperbolic type
KW - Nonlinear equations of second order
KW - Potential flow equation
KW - Shock diffraction
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U2 - 10.1137/19M1284531
DO - 10.1137/19M1284531
M3 - 21_Publication in refereed journal
VL - 52
SP - 1096
EP - 1114
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 2
ER -