Self-Similar Radially Symmetric Solutions of the Relativistic Euler Equations with Synge Energy
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914168793202688 |
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| author | Ruggeri, Tommaso Thein, Ferdinand Xiao, Qinghua |
| author_facet | Ruggeri, Tommaso Thein, Ferdinand Xiao, Qinghua |
| contents | We consider self-similar, radially symmetric solutions of the relativistic Euler equations with constitutive relations from relativistic kinetic theory, based on Synge energies for monatomic and its extension to diatomic gases. For the corresponding initial--boundary value problem, including the spherical piston problem, we prove existence and uniqueness of solutions valid for all values of the relativistic parameter $γ= mc^{2}/(k_{B}T)$, thus covering both the classical limit $(γ\to \infty)$ and the ultra-relativistic regime $(γ\to 0)$. We further establish key structural properties of Synge energies, showing the strict negativity of the second derivative with respect to pressure at constant entropy and the monotone dependence of the characteristic velocity on $γ$. These results extend the classical theory of self-similar flows to the relativistic framework with kinetic-theory-based constitutive equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Similar Radially Symmetric Solutions of the Relativistic Euler Equations with Synge Energy Ruggeri, Tommaso Thein, Ferdinand Xiao, Qinghua Analysis of PDEs Mathematical Physics Fluid Dynamics 35L40, 76N10, 76N15 We consider self-similar, radially symmetric solutions of the relativistic Euler equations with constitutive relations from relativistic kinetic theory, based on Synge energies for monatomic and its extension to diatomic gases. For the corresponding initial--boundary value problem, including the spherical piston problem, we prove existence and uniqueness of solutions valid for all values of the relativistic parameter $γ= mc^{2}/(k_{B}T)$, thus covering both the classical limit $(γ\to \infty)$ and the ultra-relativistic regime $(γ\to 0)$. We further establish key structural properties of Synge energies, showing the strict negativity of the second derivative with respect to pressure at constant entropy and the monotone dependence of the characteristic velocity on $γ$. These results extend the classical theory of self-similar flows to the relativistic framework with kinetic-theory-based constitutive equations. |
| title | Self-Similar Radially Symmetric Solutions of the Relativistic Euler Equations with Synge Energy |
| topic | Analysis of PDEs Mathematical Physics Fluid Dynamics 35L40, 76N10, 76N15 |
| url | https://arxiv.org/abs/2511.18971 |