Improved low regularity theory for gravity-capillary waves
| Autor: | Ai, Albert |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This article concerns the Cauchy problem for the gravity-capillary water waves system in general dimensions. We establish local well-posedness for initial data in $H^s$, with $s > \frac{d}{2} + 2 - \mu$, with $\mu = \frac{3}{14}$ and $\mu = \frac37$ in the cases $d = 1$ and $d \geq 2$ respectively. This represents an improvement over the the state-of-the-art low regularity theory in $d \geq 2$ dimensions. Comment: 14 pages |
| Databáze: | arXiv |
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