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Global Bifurcation of Steady Surface Capillary Waves on a $2D$ Droplet

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arxiv 2407.16794 v1 pith:MUXQD4MN submitted 2024-07-23 math.AP

classification math.AP
keywords globalrotationalsurfacewavesbifurcationequationsfluidsymmetry
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abstract

We construct global curves of rotational traveling wave solutions to the $2D$ water wave equations on a compact domain. The real analytic interface is subject to surface tension, while gravitational effects are ignored. In contrast to the rotational surface waves, the fluid flow follows the incompressible, irrotational Euler equations. This model can provide a description for tiny water droplets in breaking waves and white caps. The primary tool we use is global bifurcation theory, via a conformal formulation of the problem. The obtained fluid domains have $m$-fold discrete rotational symmetry, as well as a reflection symmetry.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Two-dimensional capillary liquid drop: Craig-Sulem formulation on $\mathbb{T}^1$ and bifurcations from multiple eigenvalues of rotating waves

    math.AP 2025-05 conditional novelty 7.0 of 10

    For small angular momentum, there exists a unique rotation orbit of smooth rotating capillary drop solutions near the circle, built by a variational bifurcation argument from a multiple eigenvalue.

  2. Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions

    math.AP 2025-06 conditional novelty 6.0 of 10

    For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.

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