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arXiv · 2610.35129

Smooth stationary water waves with multiple vortex spikes

Zhiqiang Fan·Yuchen Wang·Youquan Zheng
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Abstract

For any prescribed positive integer $n$, we establish the existence of a family of stationary solutions to the two dimensional capillary-gravity water wave equations in finite depth, whose stream functions exhibit $n$ well-separated vertically aligned vortex spikes with alternating signs. The construction is based on a nonlinear gluing scheme for a singularly perturbed semilinear elliptic equation coupled to the Bernoulli equation on the free surface. Our results extend the single-spike construction to arbitrary finite multi-spike configurations and reveal a mechanism through which exponentially localized vortex spikes can coexist with an almost flat free surface.

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Zhiqiang Fan, Yuchen Wang, Youquan Zheng. 2026-10-26. Smooth stationary water waves with multiple vortex spikes. https://arxiv.org/abs/2610.35129

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