Three-Dimensional Steady Supersonic Euler Flow Past a Concave Cornered Wedge with Lower Pressure at the Downstream

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)431-476
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume228
Issue number2
Online published21 Nov 2017
Publication statusPublished - May 2018

Abstract

In this paper, we study the stability of the three-dimensional jet created by a supersonic flow past a concave cornered wedge with the lower pressure at the downstream. The gas beyond the jet boundary is assumed to be static. It can be formulated as a nonlinear hyperbolic free boundary problem in a cornered domain with two characteristic free boundaries of different types: one is the rarefaction wave, while the other one is the contact discontinuity, which can be either a vortex sheet or an entropy wave. A more delicate argument is developed to establish the existence and stability of the square jet structure under the perturbation of the supersonic incoming flow and the pressure at the downstream. The methods and techniques developed here are also helpful for other problems involving similar difficulties.