Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909445044305920 |
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| author | Wan, Lizhe |
| author_facet | Wan, Lizhe |
| contents | We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. It is also a $\frac{1}{4}$ improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09347 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity Wan, Lizhe Analysis of PDEs 76B15, 35Q31 We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. It is also a $\frac{1}{4}$ improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17]. |
| title | Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity |
| topic | Analysis of PDEs 76B15, 35Q31 |
| url | https://arxiv.org/abs/2312.09347 |