超声速绕流固体斜坡的Prandtl-Meyer反射
Prandtl-Meyer Reflection for Supersonic Flow past a Solid Ramp
摘要：
本文介绍了我们最近关于超音速势流流过固体斜坡时的普朗特-迈耶反射的结果。当定常超音速流通过固体斜坡时，有两种可能的构型：弱激波解和强激波解。Elling-Liu定理（2008）指出，对于由势流的某些假设确定的一类物理参数，定常超音速弱激波解可以看作非定常流的长时间渐近解。本文讨论了我们最近在消除这些假设和建立定常超音速弱激波解的稳定性定理作为非定常流对势流所有物理参数的长时间渐近性方面的进展。我们应用新的数学技术，在我们最近的工作中得到的单调性和一致的先验估计弱解，这使我们能够采用勒雷-绍德尔度参数完成理论的一般情况下。
英文摘要：
We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong shock solution. Elling-Liu's theorem (2008) indicates that the steady supersonic weak shock solution can be regarded as a long-time asymptotics of an unsteady flow for a class of physical parameters determined by certain assumptions for potential flow. In this paper we discuss our recent progress in removing these assumptions and establishing the stability theorem for steady supersonic weak shock solutions as the long-time asymptotics of unsteady flows for all the physical parameters for potential flow. We apply new mathematical techniques developed in our recent work to obtain monotonicity properties and uniform apriori estimates for weak solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for the general case.
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