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

2025/08/07 by Sandine, Ely
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05817

Abstract

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<(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<(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.

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