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On the dynamical law of the GinzburgLandau vortices on the plane

FH Lin Jack Xin

Analysis of PDEs mathscidoc:1912.43854

Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 52, (10), 1189-1212, 1999.10
Abstract We study the GinzburgLandau equation on the plane with initial data being the product of n wellseparated+ 1 vortices and spatially decaying perturbations. If the separation distances are O ( 1), l, we prove that the n vortices do not move on the time scale O(^2),=o(1\over); instead, they move on the time scale O(^-21\over) according to the law j= xj W, W= l j log| xl xj|, xj=(j, j) 2, the location of the jth 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. John & Wiley Sons, Inc.
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@inproceedings{fh1999on,
  title={On the dynamical law of the GinzburgLandau vortices on the plane},
  author={FH Lin, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210223520374418},
  booktitle={Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences},
  volume={52},
  number={10},
  pages={1189-1212},
  year={1999},
}
FH Lin, and Jack Xin. On the dynamical law of the GinzburgLandau vortices on the plane. 1999. Vol. 52. In Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences. pp.1189-1212. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210223520374418.
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