Deep-water limit of the intermediate long wave equation in $L^2$

Andreia Chapouto; Guopeng Li; Tadahiro Oh; Didier Pilod

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arXiv · 2311.07997

Deep-water limit of the intermediate long wave equation in $L^2$

Andreia Chapouto·Guopeng Li·Tadahiro Oh·Didier Pilod

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Abstract

We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the $L^2$ well-posedness argument for BO by Molinet and the fourth author (2012), we prove global well-posedness of ILW in $L^2$ on both the real line and the circle. In the periodic setting, this provides the first low regularity well-posedness of ILW. We then establish convergence of the ILW dynamics to the BO dynamics in the deep-water limit at the $L^2$-level.

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Andreia Chapouto, Guopeng Li, Tadahiro Oh, Didier Pilod. 2023-11-14. Deep-water limit of the intermediate long wave equation in $L^2$. https://arxiv.org/abs/2311.07997

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