Converging/diverging self-similar shock waves: from collapse to reflection
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910371740123136 |
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| author | Jang, Juhi Liu, Jiaqi Schrecker, Matthew |
| author_facet | Jang, Juhi Liu, Jiaqi Schrecker, Matthew |
| contents | We solve the continuation problem for the non-isentropic 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 $γ\in(1,3]$ 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 $γ\in(1,\frac53]$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Converging/diverging self-similar shock waves: from collapse to reflection Jang, Juhi Liu, Jiaqi Schrecker, Matthew Analysis of PDEs We solve the continuation problem for the non-isentropic 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 $γ\in(1,3]$ 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 $γ\in(1,\frac53]$, 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. |
| title | Converging/diverging self-similar shock waves: from collapse to reflection |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.12247 |