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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00129 |
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| _version_ | 1866910851725787136 |
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| author | Erdoğan, M. B. Tzirakis, N. |
| author_facet | Erdoğan, M. B. Tzirakis, N. |
| contents | In this paper we study the Zakharov system on the upper half--plane $U=\{(x ,y)\in \R^2: y>0\}$ with non-homogenous boundary conditions. In particular we obtain low regularity local well--posedness using the restricted norm method of Bourgain and the Fourier--Laplace method of solving initial and boundary value problems. Moreover we prove that the nonlinear part of the solution is in a smoother space than the initial data. To our knowledge this is the first paper which establishes low regularity results for the 2d initial-boundary value Zakharov system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Zakharov System on the Upper Half-Plane Erdoğan, M. B. Tzirakis, N. Analysis of PDEs In this paper we study the Zakharov system on the upper half--plane $U=\{(x ,y)\in \R^2: y>0\}$ with non-homogenous boundary conditions. In particular we obtain low regularity local well--posedness using the restricted norm method of Bourgain and the Fourier--Laplace method of solving initial and boundary value problems. Moreover we prove that the nonlinear part of the solution is in a smoother space than the initial data. To our knowledge this is the first paper which establishes low regularity results for the 2d initial-boundary value Zakharov system. |
| title | The Zakharov System on the Upper Half-Plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.00129 |