2022/12/16 by Anatole Guérin, Guérin, Anatole
Mathematics · Engineering · Computer Science · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2212.08569
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.