2023/10/29 by Ely Sandine, Sandine, Ely
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2310.18870
openalex publication_date 2023/10/29 · openalex created_date 2023/11/01 · openalex updated_date 2026/08/01
Our result is a construction of infinitely many radial self-similar implosion profiles for the gravitational Euler-Poisson system. The problem can be expressed as solving a system of non-autonomous non-linear ODEs. The first rigorous existence result for a non-trivial solution to these ODEs is due to Guo, Hadžić and Jang [Comm. Math. Phys. 386.3 (2021)], in which they construct a solution found numerically by Larson and Penston independently [Monthly Notices of the Royal Astronomical Society 145.3 (1969), Monthly Notices of the Royal Astronomical Society 144.4 (1969)]. The solutions we construct belong to a different regime and correspond to a strict subset of the family of profiles discovered numerically by Hunter. Our proof adapts a technique developed by Collot, Raphaël and Szeftel in [Mem. Amer. Math. Soc. 260.1255 (2019)], in which they study blowup for a family of energy-supercritical focusing semilinear heat equations. In our case, the quasilinearity presents complications, most severely near the sonic point where the system degenerates.