Self-similar imploding solutions of the relativistic Euler equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910370675818496 |
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| author | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| author_facet | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| contents | Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\frac1\ell\varrho$ for \textit{all} $\ell>1$ in physical space dimension $d=2,3$ and for $\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving the long-standing problem: finite time blow-up of the supercritical defocusing nonlinear wave equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar imploding solutions of the relativistic Euler equations Shao, Feng Wei, Dongyi Zhang, Zhifei Analysis of PDEs Mathematical Physics Motivated by recent breakthrough on smooth imploding solutions of compressible Euler, we construct self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\frac1\ell\varrho$ for \textit{all} $\ell>1$ in physical space dimension $d=2,3$ and for $\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving the long-standing problem: finite time blow-up of the supercritical defocusing nonlinear wave equation. |
| title | Self-similar imploding solutions of the relativistic Euler equations |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2403.11471 |