Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow
Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow
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DOI：
10.1137/19m1284531
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Gui-Qiang G. Chen;M. Feldman;Jingchen Hu;Wei Xiang
中科院分区：
文献类型：
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作者：
Gui-Qiang G. Chen;M. Feldman;Jingchen Hu;Wei Xiang
本文研究了凸角楔激波衍射的Lighthill问题解的正则性，该问题可表示为自由边界问题。本文证明了势流在楔角处不存在亚音速的正则解。这表明，如果解在楔角处是亚音速的，预计至少会产生一个特征不连续（涡片或熵波），这与实验和计算结果是一致的。为了得到不存在的结果，建立了解的弱极大值原理，并发展了其他一些数学技巧。这里所开发的方法和技术对其他具有类似困难的问题也很有用。
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.