发表机构
Department of Mathematics, Shanghai University（上海大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非均匀来流下直楔形体斜声速激波的稳定性，将其归结为退化双曲自由边界问题，用Ascoli-Arzelà定理和对角线论证构造局部Lipschitz连续解，并通过加权特征分解方法克服声速线上的退化困难。
AI 中文摘要
当均匀稳态超声速来流冲击直楔形体时，若楔角小于脱体角，流场中将形成两类满足熵条件的稳态斜激波：下游流动为超声速或亚声速的弱激波，以及下游流动为亚声速的强激波。关于下游流动为亚声速或超声速的斜激波稳定性已有许多结果。然而，由于激波后的流动对扰动非常敏感，关于下游流动为声速的斜激波稳定性的研究则少得多。本文在直楔形体且来流非均匀的假设下，研究斜声速激波的稳定性。我们将问题归结为一个退化双曲型自由边界问题。利用经典Ascoli-Arzelà定理和对角线论证，构造了该自由边界问题的一个具有声速-超声速下游流动的局部Lipschitz连续解。该自由边界问题的主要困难在于声速线上的双曲退化。通过采用加权特征分解方法，我们建立了声速线附近下游流动的精细估计。
英文摘要
When a uniform steady supersonic oncoming flow impinges on a straight wedge, if the wedge angle is smaller than the detachment angle, two types of steady oblique shocks satisfying the entropy condition will form in the flow field: weak shocks with supersonic or subsonic downstream flow, and strong shocks with subsonic downstream flow. There have been many results on the stability of oblique shocks with subsonic or supersonic downstream flow. However, much less is known about the stability of oblique shocks with sonic downstream flow, since the flow behind the shock wave is very sensitive to disturbances. This paper investigates the stability of oblique sonic shocks under the assumption of a straight wedge with non-uniform incoming flow. We reduce the problem to a degenerate hyperbolic free boundary problem. A local Lipschitz-continuous solution with sonic-supersonic downstream flow to the free boundary problem is constructed, using the classical Ascoli-Arzelà theorem and a diagonal argument. The main difficulty of this free boundary problem lies in the hyperbolic degeneracy on the sonic line. By adopting a weighted characteristic decomposition method, we establish a delicate estimate of the downstream flow near the sonic line.
