Abstract
The aim of this article is to establish a concise proof for a stability result of self-similar solutions of the binormal flow, in some more restrictive cases than in Banica and Vega (Ann Sci Éc Norm Supér 48:1421–1453, 2015). This equation, also known as the Local Induction Approximation, is a standard model for vortex filament dynamics, and its self-similar solution describes the formation of a corner singularity on the filament. Our approach strongly uses the link that Hasimoto pointed out in 1972 between the solution of the binormal flow and the one of the 1-D cubic Schrödinger equation, as well as the existence results associated to the latter.
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Acknowledgements
This paper has been written during my Ph.D. under the supervision of Valeria Banica and Nicolas Burq, I would like to thank them for their precious help and discussions. I am also grateful for the relevant comments of the reviewer.
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Guérin, A. On self-similar singularity formation for the binormal flow. J. Evol. Equ. 23, 47 (2023). https://doi.org/10.1007/s00028-023-00897-9
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DOI: https://doi.org/10.1007/s00028-023-00897-9