English

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 nn equally spaced vortices with degrees ±1\pm 1. 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 ε\varepsilon 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}
}