Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908481985970176 |
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| author | Sandine, Ely |
| author_facet | Sandine, Ely |
| contents | We rigorously construct a family of smooth self-similar solutions to the isentropic gravitational Euler-Poisson system with a polytropic equation of state for polytropic indices lying in the full energy-supercritical range, $1<γ<\frac{6}{5}$. The result is an extension of the author's previous construction of Hunter solutions in the isothermal case, $γ=1$, and complements a construction of Larson-Penston-type solutions by Guo-Hadžić-Jang-Schrecker for the same system in the full mass-supercritical range, $1<γ<\frac{4}{3}$. As an ingredient in the proof, a general framework is introduced for proving local analyticity of solutions to this system in the vicinity of singular points. This framework could be used for other quasilinear self-similar blow-up constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State Sandine, Ely Analysis of PDEs We rigorously construct a family of smooth self-similar solutions to the isentropic gravitational Euler-Poisson system with a polytropic equation of state for polytropic indices lying in the full energy-supercritical range, $1<γ<\frac{6}{5}$. The result is an extension of the author's previous construction of Hunter solutions in the isothermal case, $γ=1$, and complements a construction of Larson-Penston-type solutions by Guo-Hadžić-Jang-Schrecker for the same system in the full mass-supercritical range, $1<γ<\frac{4}{3}$. As an ingredient in the proof, a general framework is introduced for proving local analyticity of solutions to this system in the vicinity of singular points. This framework could be used for other quasilinear self-similar blow-up constructions. |
| title | Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.05817 |