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arXiv · 1712.07821

Low regularity solutions for gravity water waves

Albert Ai
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Abstract

We prove local well-posedness for the gravity water waves equations without surface tension, with initial velocity field in $H^s$, $s > \frac{d}{2} + 1 - μ$, where $μ= \frac{1}{10}$ in the case $d = 1$ and $μ= \frac{1}{5}$ in the case $d \geq 2$, extending previous results of Alazard-Burq-Zuily. The improvement primarily arises in two areas. First, we perform an improved analysis of the regularity of the change of variables from Eulerian to Lagrangian coordinates. Second, we perform a time-interval length optimization of the localized Strichartz estimates.

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Albert Ai. 2018-09-26. Low regularity solutions for gravity water waves. https://doi.org/10.1007/s42286-019-00002-z

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