Self-stretching of perturbed vortex filaments. II: Structure of solutions

DOI10.1016/0167-2789(91)90066-IzbMath0752.35068OpenAlexW1559186748MaRDI QIDQ1181374

Andrew J. Majda, Rupert Klein

Publication date: 27 June 1992

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(91)90066-i

zbMATH Keywords

exact solutionsnumerical computations

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Navier-Stokes equations (35Q30) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbation theories for operators and differential equations in quantum theory (81Q15) Isotropic turbulence; homogeneous turbulence (76F05) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20)

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Cites Work

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• The evolution of a turbulent vortex
• Self-stretching of a perturbed vortex filament. I: The asymptotic equation for deviations from a straight line
• Self-stretching of perturbed vortex filaments. II: Structure of solutions
• Viscous vortical flows
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Vorticity and the mathematical theory of incompressible fluid flow
• Collapse and amplification of a vortex filament
• Vorticity, Turbulence, and Acoustics in Fluid Flow
• Asymptotic equations for the stretching of vortex filaments in a background flow field
• The instability of short waves on a vortex ring
• The inverse scattering transform: Semi-infinite interval
• The disintegration of wave trains on deep water Part 1. Theory
• A soliton on a vortex filament
• On the stability of vortex rings