Self-binormal solutions of the Localized Induction Approximation: Singularity formation

Details Self-binormal solutions of the Localized Induction Approximation: Singularity formation Self-binormal solutions of the Localized Induction Approximation: Singularity formation

2004-04-16

arxiv.org/abs/math/0404291v1

Mathematics

Analysis of PDEs

60 pages, 8 figures

Scientific paper

10.1088/0951-7715/17/6/006

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.

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