Solutions to the master equations governing fractional vortices
Journal
Journal of Differential Equations
Journal Volume
254
Journal Issue
3
Pages
1437-1463
Date Issued
2013
Author(s)
Abstract
By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing 'fractional multiple vortices.' In the doubly periodic situation, the conditions for existence are both necessary and sufficient and give the upper bounds for the vortex numbers in terms of the size of the periodic cell domain. In the planar situation, there is no restriction on the vortex numbers. In both situations, the solutions are uniquely determined by the prescribed locations and the local winding numbers of the vortices. © 2012 Elsevier Inc.
Type
journal article