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Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system
- Publication Year :
- 2016
-
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.
- Subjects :
- Mathematics - Analysis of PDEs
35B35, 35L70, 35Q31, 35Q75
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1605.08083
- Document Type :
- Working Paper