The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution
Dynamical Systems
2014-05-27 v2 Analysis of PDEs
Abstract
We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of equally spaced vortices with degrees . In particular we prove the existence of such solutions when the surface is longitudinally symmetric. Then we seek a rotating solution to the Gross-Pitaevskii equation having vortices that follow those of the point-vortex flow for sufficiently small.
Keywords
Cite
@article{arxiv.1401.5544,
title = {The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution},
author = {Ko-Shin Chen},
journal= {arXiv preprint arXiv:1401.5544},
year = {2014}
}