Nonlinear Stability of Expanding Star Solutions of the Radially Symmetric Mass‐Critical Euler‐Poisson System

Abstract

Abstract We prove nonlinear stability of compactly supported expanding star solutions of the mass‐critical gravitational Euler‐Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expansion rate of such solutions can be either self‐similar or non‐self‐similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global‐in‐time radially symmetric solutions, which are not homologous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free‐boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass‐critical with respect to an invariant rescaling and the analysis is carried out in similarity variables. © 2017 Wiley Periodicals, Inc.