Nonradial stability of expanding Goldreich-Weber stars
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910443205820416 |
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| author | Hadžić, Mahir Jang, Juhi Lam, King Ming |
| author_facet | Hadžić, Mahir Jang, Juhi Lam, King Ming |
| contents | Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $λ(t)_{t\to\infty}\sim t^{\frac23}$ and linear rate $λ(t)_{t\to\infty}\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable against irrotational perturbations.
The codimension-4 condition in the latter result is optimal and reflects the presence of 4 unstable directions in the linearised dynamics in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as a codimension-1 nonlinear stability of the moduli space of self-similarly expanding Goldreich-Weber stars against irrotational perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11420 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonradial stability of expanding Goldreich-Weber stars Hadžić, Mahir Jang, Juhi Lam, King Ming Analysis of PDEs 35Q85, 35Q35, 35Q31, 35B35, 76N10 Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $λ(t)_{t\to\infty}\sim t^{\frac23}$ and linear rate $λ(t)_{t\to\infty}\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable against irrotational perturbations. The codimension-4 condition in the latter result is optimal and reflects the presence of 4 unstable directions in the linearised dynamics in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as a codimension-1 nonlinear stability of the moduli space of self-similarly expanding Goldreich-Weber stars against irrotational perturbations. |
| title | Nonradial stability of expanding Goldreich-Weber stars |
| topic | Analysis of PDEs 35Q85, 35Q35, 35Q31, 35B35, 76N10 |
| url | https://arxiv.org/abs/2212.11420 |