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Evolution of viscous vortex filaments and desingularization of the Biot-Savart integral

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arxiv 2311.12246 v1 pith:RYHC5T5F submitted 2023-11-21 math.AP math-phmath.MP

Marco A. Fontelos , Luis Vega This is my paper · ORCID
classification math.APmath-phmath.MP
keywords filamentvortexgammaorderviscousachievebinormalbiot-savart
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abstract

We consider a viscous fluid with kinematic viscosity $\nu $ and initial data consisting of a smooth closed vortex filament with circulation $\Gamma $. We show that, for short enough time, the solution consists of a deformed Lamb-Oseen vortex whose center (a filament) follows the binormal flow dynamics plus leading order corrections that depend locally on the filament curvature and the nonlocal interactions with distant parts of the filament. In order to achieve this scale separation we require $\Gamma /\nu $ to be sufficiently small.

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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. Evolution of viscous vortex filaments and soliton-type propagation

    math.AP 2026-07 conditional novelty 6.0 of 10

    For small circulation and short times, Navier–Stokes vorticity concentrated on an open curve is rigorously a Lamb–Oseen profile around a binormal-flow curve, with uniform error estimates that allow large torsion.

  2. Turbulent solutions of the binormal flow and the 1D cubic Schr\"odinger equation

    math.AP 2024-12 unverdicted novelty 1.0 of 10

    A self-survey of the authors' proofs that the binormal flow and 1D cubic NLS admit solutions with turbulent features like multifractality and Talbot effects.

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