Propagation Estimates for the Boson Star Equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911335845986304 |
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| author | Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana |
| author_facet | Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana |
| contents | We consider the boson star equation with a general two-body interaction potential $w$ and initial data $ψ_0$ in a Sobolev space. Under general assumptions on $w$, namely that $w$ decomposes as a sum of a finite, signed measure and an essentially bounded function, we prove that the (local in time) solution cannot propagate faster than the speed of light, up to a sharp exponentially small remainder term. If $w$ is short-range and $ψ_0$ is regular and small enough, we prove in addition asymptotic phase-space propagation estimates and minimal velocity estimates for the (global in time) solution, depending on the momentum of the scattering state associated to $ψ_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation Estimates for the Boson Star Equation Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana Mathematical Physics Analysis of PDEs We consider the boson star equation with a general two-body interaction potential $w$ and initial data $ψ_0$ in a Sobolev space. Under general assumptions on $w$, namely that $w$ decomposes as a sum of a finite, signed measure and an essentially bounded function, we prove that the (local in time) solution cannot propagate faster than the speed of light, up to a sharp exponentially small remainder term. If $w$ is short-range and $ψ_0$ is regular and small enough, we prove in addition asymptotic phase-space propagation estimates and minimal velocity estimates for the (global in time) solution, depending on the momentum of the scattering state associated to $ψ_0$. |
| title | Propagation Estimates for the Boson Star Equation |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2512.20718 |