Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow.
Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow.
复制标题
DOI：
--
复制
发表时间：
2019-03
期刊：
影响因子：
--
通讯作者：
Gui-Qiang G. Chen;M. Feldman;Wei Xiang
中科院分区：
文献类型：
--
作者：
Gui-Qiang G. Chen;M. Feldman;Wei Xiang
当平面激波正面撞击二维楔块时，它会经历反射-衍射过程，然后随着原始激波及时向前移动，自相似的反射激波向外移动。实验、计算和渐近分析表明存在各种模式，包括规则反射和马赫反射。冯·诺依曼关于从规则反射到马赫反射的转变的猜想涉及规则激波反射-衍射配置的存在性、唯一性和稳定性，该配置是由可压缩流动的凹角楔块生成的。在本文中，我们讨论冯诺依曼猜想研究的一些最新进展。更具体地说，我们介绍了由适当类别的解中的势流方程控制的规则冲击反射-衍射配置的独特性和稳定性的最新结果。我们首先证明 Chen-Feldman [19] 获得的全局解中的跨音速激波是凸的。然后，我们针对任何大于脱离角或临界角的楔角，建立了具有凸跨音速激波的全局激波反射-衍射配置的唯一性。此外，还显示了解相对于楔角的稳定性。我们的方法还提供了另一种方法来证明[19]中首先建立的可接受解的存在性。
When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic analysis has indicated that various patterns occur, including regular reflection and Mach reflection. The von Neumann conjectures on the transition from regular to Mach reflection involve the existence, uniqueness, and stability of regular shock reflection-diffraction configurations, generated by concave cornered wedges for compressible flow. In this paper, we discuss some recent developments in the study of the von Neumann conjectures. More specifically, we present our recent results of the uniqueness and stability of regular shock reflection-diffraction configurations governed by the potential flow equation in an appropriate class of solutions. We first show that the transonic shocks in the global solutions obtained in Chen-Feldman [19] are convex. Then we establish the uniqueness of global shock reflection-diffraction configurations with convex transonic shocks for any wedge angle larger than the detachment angle or the critical angle. Moreover, the stability of the solutions with respect to the wedge angle is also shown. Our approach also provides an alternative way of proving the existence of the admissible solutions established first in [19].