Self-binormal solutions of the Localized Induction Approximation: Singularity formation
Preprint
Abstract
We investigate the formation of singularities in a self-similar form of regular solutions of the Localized Induction Approximation (also referred as to the binormal flow). This equation appears as an approximation model for the self-induced motion of a vortex filament in an inviscid incompressible fluid. The solutions behave as 3d-logarithmic spirals at infinity. The proofs of the results are strongly based on the existing connection between the binormal flow and certain Schr\"odinger equations.Keywords
All Related Versions
- Version 1, 2004-04-16, ArXiv
- Published version: Nonlinearity, 17 (6), 2091.
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