Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912718579040256 |
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| author | Chen, Geng El-Katri, Faris A. Hu, Yanbo Shen, Yannan |
| author_facet | Chen, Geng El-Katri, Faris A. Hu, Yanbo Shen, Yannan |
| contents | In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the invariant domain idea, we show that, for polytropic ideal gases with $γ\geq3$, the smooth solution develops a singularity in finite time for a class of initial supersonic inward waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry Chen, Geng El-Katri, Faris A. Hu, Yanbo Shen, Yannan Analysis of PDEs 76N15, 35L65, 35L67 In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the invariant domain idea, we show that, for polytropic ideal gases with $γ\geq3$, the smooth solution develops a singularity in finite time for a class of initial supersonic inward waves. |
| title | Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry |
| topic | Analysis of PDEs 76N15, 35L65, 35L67 |
| url | https://arxiv.org/abs/2511.15180 |