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arXiv · 2312.09347

Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

Lizhe Wan
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Abstract

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].

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Lizhe Wan. 2023-12-14. Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity. https://arxiv.org/abs/2312.09347

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