Existence and singularity formation for the supersonic expanding wave of radially symmetric non-isentropic compressible Euler equations
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| Format: | Preprint |
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2026
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| _version_ | 1866912958304485376 |
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| author | Chen, Geng El-Katri, Faris A. Hu, Yanbo |
| author_facet | Chen, Geng El-Katri, Faris A. Hu, Yanbo |
| contents | This paper studies the existence and singularity formation of supersonic expanding waves for the radially symmetric non-isentropic compressible Euler equations of polytropic gases. We introduce a suitable pair of gradient variables to characterize the rarefaction and compression properties of the solutions. Based on their Riccati equations, we construct several useful invariant domains to establish a series of priori estimates of solutions under some assumptions on the initial data. We show that the solution is smooth in the characteristic triangle or quadrangle domain if both of these two gradient variables are non-negative at the initial time. On the other hand, when one of these two variables is very negative at some initial point, the solution forms a singularity in finite time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_09199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and singularity formation for the supersonic expanding wave of radially symmetric non-isentropic compressible Euler equations Chen, Geng El-Katri, Faris A. Hu, Yanbo Analysis of PDEs This paper studies the existence and singularity formation of supersonic expanding waves for the radially symmetric non-isentropic compressible Euler equations of polytropic gases. We introduce a suitable pair of gradient variables to characterize the rarefaction and compression properties of the solutions. Based on their Riccati equations, we construct several useful invariant domains to establish a series of priori estimates of solutions under some assumptions on the initial data. We show that the solution is smooth in the characteristic triangle or quadrangle domain if both of these two gradient variables are non-negative at the initial time. On the other hand, when one of these two variables is very negative at some initial point, the solution forms a singularity in finite time. |
| title | Existence and singularity formation for the supersonic expanding wave of radially symmetric non-isentropic compressible Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.09199 |