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Steady vortex sheets in presence of surface tension

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arxiv 2410.12612 v1 pith:4B45C7ER submitted 2024-10-16 math.AP

Federico Murgante , Emeric Roulley , Stefano Scrobogna This is my paper · ORCID
classification math.AP
keywords surfacetensionbifurcationsheetsvortexaccountcircularcoefficient
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We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation parameters, we play with either the speed of rotation, the surface tension coefficient or the mean vorticity.

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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. Long-time dynamics for the Kelvin-Helmholtz equations close to circular vortex sheets

    math.AP 2025-04 conditional novelty 8.0 of 10

    For almost all Weber numbers below 4(2+sqrt(3)), small-amplitude circular vortex sheets with surface tension stay O(ε)-close to the circular equilibrium for times of order ε^{-(N+1)} for every integer N.

  2. 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.

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