Low regularity well-posedness for two-dimensional hydroelastic waves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915694954676224 |
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| author | Wan, Lizhe Yang, Jiaqi |
| author_facet | Wan, Lizhe Yang, Jiaqi |
| contents | We investigate the low regularity local well-posedness of two-dimensional irrotational deep hydroelastic waves. Building on the approach of Ifrim-Tataru [29] and Ai-Ifrim-Tataru [5], in particular by constructing a cubic modified energy that incorporates a paradifferential weight chosen carefully, we prove that the hydroelastic waves are locally well-posed in $\mathcal{H}^s$ for $s>\frac{3}{4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low regularity well-posedness for two-dimensional hydroelastic waves Wan, Lizhe Yang, Jiaqi Analysis of PDEs 76B15, 74F10, 76B07 We investigate the low regularity local well-posedness of two-dimensional irrotational deep hydroelastic waves. Building on the approach of Ifrim-Tataru [29] and Ai-Ifrim-Tataru [5], in particular by constructing a cubic modified energy that incorporates a paradifferential weight chosen carefully, we prove that the hydroelastic waves are locally well-posed in $\mathcal{H}^s$ for $s>\frac{3}{4}$. |
| title | Low regularity well-posedness for two-dimensional hydroelastic waves |
| topic | Analysis of PDEs 76B15, 74F10, 76B07 |
| url | https://arxiv.org/abs/2512.22040 |