Selfsimilar solutions of the binormal flow and their stability
Valeria Banica, Luis Vega
TL;DR
This paper reviews recent findings on vortex filament evolution, focusing on self-similar solutions of the binormal flow and analyzing their stability in relation to the cubic nonlinear Schrödinger equation.
Contribution
It provides a comprehensive review of self-similar solutions and investigates their stability, connecting vortex filament dynamics with nonlinear Schrödinger equations.
Findings
Identification of self-similar solutions of the binormal flow
Analysis of stability properties of these solutions
Connection established between vortex filament evolution and nonlinear Schrödinger equation
Abstract
We review some recent results concerning the evolution of a vortex filament and its relation to the cubic non-linear Schr\"odinger equation. Selfsimilar solutions and questions related to their stability are studied.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Navier-Stokes equation solutions