Abstract
We solve the continuation problem for the nonisentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Güderley imploding shock solutions for a perfect gas with adiabatic exponent γ ∊ (1, 3] admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for γ ∊ (1, 5 3 ], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.
| Original language | English |
|---|---|
| Pages (from-to) | 190-232 |
| Number of pages | 43 |
| Journal | Siam Journal on Mathematical Analysis |
| Volume | 57 |
| Issue number | 1 |
| Early online date | 6 Jan 2025 |
| DOIs | |
| Publication status | Published - 28 Feb 2025 |
Funding
The first and second authors are supported in part by the NSF grants DMS-2009458 and DMS-2306910. The third author is supported by the EPSRC Post-doctoral Research Fellowship EP/W001888/1
| Funders | Funder number |
|---|---|
| Not added | DMS-2009458, DMS-2306910 |
| Engineering and Physical Sciences Research Council | EP/W001888/1 |
Keywords
- compressible fluid flow
- nonisentropic Euler system
- radial symmetry
- shock wave
- similarity solutions
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics