Hunter Self-Similar Implosion Profiles for the Gravitational Euler-Poisson System

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 et al. (Commun Math Phys 386(3):1551-1601, 2021), in which they construct a solution found numerically by Larson (Mon Not R Astron Soc 145(3):271-295, 1969) and Penston (Mon Not R Astron Soc 144(4):425-448, 1969) independently. The solutions we construct belong to a different regime and correspond to a strict subset of the family of profiles discovered numerically by Hunter (Astrophys J 218:834, 1977). Our proof adapts a technique developed by Collot et al. (Mem Am Math Soc 260(1255):v+97, 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.