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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/2504.09333 |
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| _version_ | 1866909578531176448 |
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| author | Herr, Sebastian Schippa, Robert Tzvetkov, Nikolay |
| author_facet | Herr, Sebastian Schippa, Robert Tzvetkov, Nikolay |
| contents | We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these at hand, we show global well-posedness of the quasilinear Cauchy problem in $L^2(\mathbb{R} \times \mathbb{T})$. Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global results for weakly dispersive KP-II equations on the cylinder Herr, Sebastian Schippa, Robert Tzvetkov, Nikolay Analysis of PDEs We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these at hand, we show global well-posedness of the quasilinear Cauchy problem in $L^2(\mathbb{R} \times \mathbb{T})$. Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case. |
| title | Global results for weakly dispersive KP-II equations on the cylinder |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.09333 |