On the vortex filament conjecture for Euler flows
Analysis of PDEs
2017-01-04 v1 Mathematical Physics
math.MP
Abstract
In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in , we prove that the curve evolves to leading order by binormal curvature flow. Our approach combines new estimates on the distance of the corresponding Hamiltonian-Possion structures with stability estimates recently developed in Ref. 15.
Cite
@article{arxiv.1603.00227,
title = {On the vortex filament conjecture for Euler flows},
author = {Robert L. Jerrard and Christian Seis},
journal= {arXiv preprint arXiv:1603.00227},
year = {2017}
}