Stability of 𝑛-vortices in the Ginzburg-Landau equation

Coleman, James

doi:10.1090/S0002-9939-00-05695-1

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ISSN 1088-6826(online) ISSN 0002-9939(print)

Stability of -vortices in the Ginzburg-Landau equation

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

We consider the class of -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 -vortices are unstable in the case $\vert n \vert \ge 2$ .

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