标题： 普朗特-梅耶反射用于超音速流绕固体斜坡的情况 显示英文标题

标题： Prandtl-Meyer Reflection for Supersonic Flow past a Solid Ramp

摘要： 我们介绍了关于超音速势流绕固体斜坡的普朗特-梅耶尔反射的最新结果。 当稳定超音速流绕过固体斜坡时，有两种可能的配置：弱激波解和强激波解。 Elling-Liu定理（2008）表明，对于由势流某些假设确定的一类物理参数，稳定超音速弱激波解可以视为非定常流的长时间渐进行为。 在本文中，我们讨论了我们在去除这些假设以及建立稳定超音速弱激波解作为所有势流物理参数下非定常流长时间渐进行为的稳定性定理方面的最新进展。 我们应用了最近工作中开发的新数学技术，以获得弱解的单调性性质和统一的先验估计，这使我们能够使用Leray-Schauder度论方法来完成一般情况下的理论。 显示英文摘要

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.