On the relationship between the one-corner problem and the \(M\)-corner problem for the vortex filament equation

DOI10.1007/s00332-018-9477-7zbMath1447.35263arXiv1707.09408OpenAlexW2741998132MaRDI QIDQ1631372

Luis Vega, Francisco de la Hoz

Publication date: 6 December 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.09408

zbMATH Keywords

turbulencevortex filament equationintermittencymultifractalitytransfer of energyTalbot effect

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for discrete and fast Fourier transforms (65T50) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractals (28A80) Vortex methods applied to problems in fluid mechanics (76M23) Second-order parabolic systems (35K40)

Related Items (13)

Riemann's non-differentiable function and the binormal curvature flow ⋮ Singularity formation for the 1-D cubic NLS and the Schrödinger map on \(\mathbb{S}^2\) ⋮ Non-conservation of dimension in divergence-free solutions of passive and active scalar systems ⋮ Reconnection of infinitely thin antiparallel vortices and coherent structures ⋮ On the Evolution of the Vortex Filament Equation for Regular $M$-Polygons with Nonzero Torsion ⋮ Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow ⋮ On the energy of critical solutions of the binormal flow ⋮ Intermittency of Riemann’s non-differentiable function through the fourth-order flatness ⋮ Unnamed Item ⋮ Asymptotics for vortex filaments using a modified Biot-Savart kernel ⋮ 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

Uses Software

• DLMF

Cites Work

• Unnamed Item
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