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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of $n$-vortices in the Ginzburg-Landau equation


Author: James Coleman
Journal: Proc. Amer. Math. Soc. 128 (2000), 1567-1569
MSC (2000): Primary 35Q55
Published electronically: February 7, 2000
MathSciNet review: 1751311
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Abstract:

We consider the class of $n$-vortex solutions to the time-independent Ginzburg-Landau equation on $\mathbf{R}^2$. We prove an inequality governing the solutions of a particular boundary value problem. This inequality is crucial for an elementary proof by Ovchinnikov and Sigal that such $n$-vortices are unstable in the case $\vert n \vert \ge 2$.


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Additional Information

James Coleman
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: coleman@math.utoronto.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05695-1
PII: S 0002-9939(00)05695-1
Received by editor(s): April 15, 1999
Published electronically: February 7, 2000
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society