标题： 猎人型聚心流形用于能量超临界多变状态方程 显示英文标题

标题： Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State

摘要： 我们严格构造了一族光滑自相似解，用于等熵引力欧拉-泊松系统，其多方状态方程的多方指数位于完整的能量超临界范围内，$1<\gamma<\frac{6}{5}$。该结果是对作者之前在等温情况下构造的Hunter解的扩展，$\gamma=1$，并补充了Guo-Hadžić-Jang-Schrecker针对同一系统在完整质量超临界范围内的Larson-Penston型解的构造，$1<\gamma<\frac{4}{3}$。作为证明中的一个组成部分，引入了一个通用框架，用于证明该系统在奇点附近的局部解析性。该框架可用于其他拟线性自相似爆破解的构造。 显示英文摘要

摘要： 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, $1<\gamma<\frac{6}{5}$. The result is an extension of the author's previous construction of Hunter solutions in the isothermal case, $\gamma=1$, and complements a construction of Larson-Penston-type solutions by Guo-Had\v{z}i\'c-Jang-Schrecker for the same system in the full mass-supercritical range, $1<\gamma<\frac{4}{3}$. 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.