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arXiv · 2604.19380

Small scale creation in 2D gravity-capillary water waves with vorticity

Yuanpeng Tu
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Abstract

In this paper, we consider 2D incompressible Euler equations in an unbounded domain with a free surface and a fixed bottom at finite depth. The fluid motion is under the influence of gravity and surface tension. We construct initial data with a flat free surface and small velocity, such that the $L^\infty$ norm of the vorticity gradient has at least a double-exponential growth rate within the lifespan of the corresponding solution. This work generalizes the result of Zlatos to the free-surface setting and Hu--Luo--Yao to the case of an unbounded domain.

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Yuanpeng Tu. 2026-04-21. Small scale creation in 2D gravity-capillary water waves with vorticity. https://arxiv.org/abs/2604.19380

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