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On the Cauchy Problem of Spherical Capillary Water Waves

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arxiv 2310.07113 v1 pith:OBSCX2F4 submitted 2023-10-11 math.AP

classification math.AP
keywords sphericalwatercapillaryequationpara-differentialsystemunderwaves
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The spherical capillary water waves equation describes the motion of an almost spherical water droplet under zero gravity governed by water-air interface tension. Using para-differential calculus on compact Lie groups and homogeneous spaces developed by the author, the system is symmetrized into a quasi-linear dispersive para-differential equation of order 1.5 defined on the 2-sphere. An immediate consequence of this symmetrization is a new proof of local well-posedness of the system under much weaker regularity assumption compared to previous results.

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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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