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Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone
- Source :
- Nagoya Math. J. 199 (2010), 151-181
- Publication Year :
- 2010
- Publisher :
- Cambridge University Press (CUP), 2010.
-
Abstract
- In this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.
- Subjects :
- Shock wave
Shock (fluid dynamics)
76N15
Astrophysics::High Energy Astrophysical Phenomena
General Mathematics
010102 general mathematics
010103 numerical & computational mathematics
Mechanics
35L70
01 natural sciences
35L67
35L65
Shock diamond
Oblique shock
Supersonic speed
Bow shock (aerodynamics)
0101 mathematics
Transonic
Ludwieg tube
Astrophysics::Galaxy Astrophysics
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 199
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....87cc7da34e4cf9e54de51173891985a5