Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system
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 expanding 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 homogeneous 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.
Keywords
Cite
@article{arxiv.1605.08083,
title = {Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system},
author = {Mahir Hadzic and Juhi Jang},
journal= {arXiv preprint arXiv:1605.08083},
year = {2016}
}