Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

TL;DR

This paper analyzes the stability of transonic jets with strong rarefaction waves in two-dimensional steady compressible Euler flows, employing wave front tracking to handle non-smooth perturbations and wave interactions.

Contribution

It establishes the structural stability of transonic jet flow patterns with strong rarefaction waves under non-smooth perturbations using a wave front tracking approach.

Findings

Proves stability of flow patterns with strong rarefaction waves.

Develops a Glimm functional for non-isentropic Euler systems.

Handles large total variation in rarefaction waves.

Abstract

We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic gas. Meanwhile, a transonic characteristic discontinuity appears to separate the supersonic flow behind the rarefaction wave from the static gas. In this paper, we employ a wave front tracking method to establish structural stability of such a flow pattern under non-smooth perturbations of the upcoming supersonic flow. It is an initial-value/free-boundary problem for the two-dimensional steady non-isentropic compressible Euler system. The main ingredients are careful analysis of wave interactions and construction of suitable Glimm functional, to overcome the difficulty that the strong rarefaction wave has a large total variation.