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.
| Original language | English |
|---|---|
| Pages (from-to) | 2911-2943 |
| Number of pages | 33 |
| Journal | Discrete and Continuous Dynamical Systems- Series A |
| Volume | 38 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2018 |
Keywords
- Characteristic discontinuity
- Compressible Euler equations
- Glimm functional
- Interaction of waves
- Rarefaction wave
- Transonic
- Wave front tracking