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arXiv · 2410.05201

Low regularity well-posedness for two-dimensional deep water waves

Lizhe Wan
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Abstract

The study of gravity-capillary water waves in two space dimensions has been an important question in mathematical fluid dynamics. By implementing the cubic modified energy method of Ifrim-Tataru in the context of gravity-capillary waves, we show that for $s> 1$, the two-dimensional gravity-capillary water wave system is locally well-posed in $\mathcal{H}^{s}$.

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Lizhe Wan. 2024-10-07. Low regularity well-posedness for two-dimensional deep water waves. https://arxiv.org/abs/2410.05201

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