On the Dynamical Law of the Ginzburg-Landau Vortices on the Plane

  title={On the Dynamical Law of the Ginzburg-Landau Vortices on the Plane},
  author={F.-H. Lin and Jack X. Xin},
We study the Ginzburg-Landau equation on the plane with initial data being the product ofn well-separated+1 vortices and spatially decaying perturbations. If the separation distances are O(ε−1), ε 1, we prove that then vortices do not move on the time scale O(ε−2λε), λε = o(log ε ); instead, they move on the time scaleO(ε−2 log ε ) according to the law ̇ xj = −∇xj W, W = −∑l 6= j log|xl −xj |, xj = (ξ j ,η j) ∈ R2, the location of thej th vortex. The main ingredients of our proof consist of… CONTINUE READING
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