Toroidal Vortex Filament Knots and Links: Existence, Stability and Dynamics

DOI10.1137/19M1307019zbMath1461.76086arXiv1912.06100OpenAlexW3096294275MaRDI QIDQ4983512

Chris Ticknor, Theodore Kolokolnikov, Panayotis G. Kevrekidis

Publication date: 20 April 2021

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

Full work available at URL: https://arxiv.org/abs/1912.06100

zbMATH Keywords

rotation frequencyKlein-Majda-Damodaran modelnear parallel vortex filaments

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47) Hydrodynamic stability (76E99)

Cites Work

• Evolution, interaction and collisions of vortex filaments.
• Relative equilibria of the \((1+N)\)-vortex problem
• Nearly parallel vortex filaments in the 3D Ginzburg-Landau equations
• Long-wave instability of a helical vortex
• A vortex filament tracking method for the Gross–Pitaevskii model of a superfluid
• The Defocusing Nonlinear Schrödinger Equation
• Maximum efficiency of wind turbine rotors using Joukowsky and Betz approaches
• Equilibrium statistical theory for nearly parallel vortex filaments
• On the stability of multiple helical vortices
• Relative equilibria of vortices in two dimensions
• Simplified equations for the interaction of nearly parallel vortex filaments
• Evolution of vortex knots
• Dynamics of nearly parallel interacting vortex filaments
• Vortex Dynamics
• A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates
• VORTICES IN BOSE–EINSTEIN CONDENSATES: SOME RECENT DEVELOPMENTS
• The \(N\)-vortex problem. Analytical techniques
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