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This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.
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Zuhan Liu (2002) studied this question.
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