Abstract
In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar dynamics of small pertubations of a given selfsimilar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic 1-D Schrödinger equation, connected to the binormal flow by Hasimoto's transform.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.