On decay and regularly of solutions of the Benjamin-Ono equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909776223404032 |
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| author | Linares, Felipe Ponce, Gustavo |
| author_facet | Linares, Felipe Ponce, Gustavo |
| contents | We study persistence properties of solutions of the Benjamin-Ono equation in weighted Sobolev spaces. Roughly, we show that for $β<7/2$, the solution $u(x,t)$ of the BO remains in the space $L^2(|x|^{2β} dx)$ if and only if its data $u(x,0)$ belongs to this space and it is regular enough, i.e. $u_0\in H^β(\mathbb R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On decay and regularly of solutions of the Benjamin-Ono equation Linares, Felipe Ponce, Gustavo Analysis of PDEs 35Q53, 35B40 We study persistence properties of solutions of the Benjamin-Ono equation in weighted Sobolev spaces. Roughly, we show that for $β<7/2$, the solution $u(x,t)$ of the BO remains in the space $L^2(|x|^{2β} dx)$ if and only if its data $u(x,0)$ belongs to this space and it is regular enough, i.e. $u_0\in H^β(\mathbb R)$. |
| title | On decay and regularly of solutions of the Benjamin-Ono equation |
| topic | Analysis of PDEs 35Q53, 35B40 |
| url | https://arxiv.org/abs/2509.06816 |