Self-binormal solutions of the Localized Induction Approximation: Singularity formation
Analysis of PDEs
2009-11-10 v1
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.
Cite
@article{arxiv.math/0404291,
title = {Self-binormal solutions of the Localized Induction Approximation: Singularity formation},
author = {Susana Gutierrez and Luis Vega},
journal= {arXiv preprint arXiv:math/0404291},
year = {2009}
}
Comments
60 pages, 8 figures