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June  2018, 38(6): 2911-2943. doi: 10.3934/dcds.2018125

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

 1 Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China 2 Department of Mathematics, Center for PDE and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China

* Corresponding author: Hairong Yuan

Received  July 2017 Revised  December 2017 Published  April 2018

Fund Project: The research of Min Ding is supported by the Fundamental Research Funds for the Central Universities (WUT: 2016IVA074) and by the National Natural Science Foundation of China under Grant Nos. 11626176 and 11701435. The research of Hairong Yuan is supported by the National Natural Science Foundation of China under Grant No. 11371141, and by Science and Technology Commission of Shanghai Municipality (STCSM) under grant No. 13dz2260400.

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.

Citation: Min Ding, Hairong Yuan. Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2911-2943. doi: 10.3934/dcds.2018125
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##### References:
A transonic characteristic discontinuity separating supersonic flow behind the rarefaction wave and the surrounding static gas.
Reflection on the free-boundary.
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