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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2510.00692 |
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| _version_ | 1866911187703169024 |
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| author | Luong, Hung |
| author_facet | Luong, Hung |
| contents | In this paper, we revisit the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. Our method is based on the dispersive estimates and the suitable Bourgain's spaces. We then, obtain the local well-posedness of the solution with the main component $ψ$ belongs to $H^1(\mathbb{R}^d)$ ($d=2, 3$) which is actually the energy space corresponding to this component. Our result also suggests a potential approach to the problem of finding exact existence time scale for the solution of Benney-Roskes model in the context of water waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system Luong, Hung Analysis of PDEs 35Q35, 35Q55 In this paper, we revisit the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. Our method is based on the dispersive estimates and the suitable Bourgain's spaces. We then, obtain the local well-posedness of the solution with the main component $ψ$ belongs to $H^1(\mathbb{R}^d)$ ($d=2, 3$) which is actually the energy space corresponding to this component. Our result also suggests a potential approach to the problem of finding exact existence time scale for the solution of Benney-Roskes model in the context of water waves. |
| title | Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system |
| topic | Analysis of PDEs 35Q35, 35Q55 |
| url | https://arxiv.org/abs/2510.00692 |