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

Susana Gutierrez·Luis Vega
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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 Schrödinger equations.

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Susana Gutierrez, Luis Vega. 2004-04-16. Self-binormal solutions of the Localized Induction Approximation: Singularity formation. https://doi.org/10.1088/0951-7715%2F17%2F6%2F006

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