On self-similar singularity formation for the binormal flow

Anatole Guérin (1, 2, 3, 4)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 LMO - Laboratoire de Mathématiques d'Orsay
3 Université Paris-Saclay
4 SU - Sorbonne Université

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 [5]. 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.

Domaines: Equations aux dérivées partielles [math.AP]

Anatole Guérin. On self-similar singularity formation for the binormal flow. 2022. ⟨hal-03903985⟩