On the Evolution of the Vortex Filament Equation for Regular $M$-Polygons with Nonzero Torsion

DOI10.1137/19M1272755zbMath1434.65201arXiv1909.01029MaRDI QIDQ5110570

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Publication date: 21 May 2020

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01029

zbMATH Keywords

turbulencevortex filament equationmultifractalityTalbot effect

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractals (28A80)

Related Items (5)

Riemann's non-differentiable function and the binormal curvature flow ⋮ On the energy of critical solutions of the binormal flow ⋮ Vortex filament equation for a regular polygon in the hyperbolic plane ⋮ On the Schrödinger map for regular helical polygons in the hyperbolic space ⋮ Convergence over fractals for the periodic Schrödinger equation

Cites Work

• On the motion of a curve by its binormal curvature
• Differentiability and dimension of some fractal Fourier series
• On the relationship between the one-corner problem and the \(M\)-corner problem for the vortex filament equation
• Fractal solutions of dispersive partial differential equations on the torus
• The spectrum of singularities of Riemann's function
• The vortex filament equation as a pseudorandom generator
• Talbot effect for the cubic non-linear Schröedinger equation on the torus
• Evolution of polygonal lines by the binormal flow
• Vortex filament equation for a regular polygon
• A Numerical Study of the Self-Similar Solutions of the Schrödinger Map
• Dispersive Quantization
• The velocity field induced by a helical vortex filament
• There is More than One Way to Frame a Curve
• The effect of torsion on the motion of a helical vortex filament
• Integer, fractional and fractal Talbot effects
• Formation of Singularities and Self-Similar Vortex Motion Under the Localized Induction Approximation†
• On the energy of critical solutions of the binormal flow
• A soliton on a vortex filament

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