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arXiv · 2405.06529

Amplitude bounds of steady rotational water waves

Susanna V. Haziot·Walter A. Strauss
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Abstract

We consider classical steady water waves with a free surface, a flat bottom and constant vorticity $\gamma$. In the adverse case $\gamma>0$ we prove that there is an absolute upper bound on the amplitude, independent of the physical constants, provided that $\gamma$ is sufficiently small. In any favorable case $\gamma\leq0$ we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as $\gamma$ tends to negative infinity.

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Susanna V. Haziot, Walter A. Strauss. 2024-05-10. Amplitude bounds of steady rotational water waves. https://arxiv.org/abs/2405.06529

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