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On the dynamical law of the Ginzburg-Landau vortices on the plane

✍ Scribed by F.-H. Lin; J. X. Xin

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
164 KB
Volume
52
Category
Article
ISSN
0010-3640

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✦ Synopsis

We study the Ginzburg-Landau equation on the plane with initial data being the product of n well-separated +1 vortices and spatially decaying perturbations. If the separation distances are O(Ξ΅ -1 ), Ξ΅ 1, we prove that the n vortices do not move on the time scale

the location of the j th vortex. The main ingredients of our proof consist of estimating the large space behavior of solutions, a monotonicity inequality for the energy density of solutions, and energy comparisons. Combining these, we overcome the infinite energy difficulty of the planar vortices to establish the dynamical law.

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