Quantization and Motion Law for Ginzburg–Landau Vortices

@article{Smets2007QuantizationAM,
  title={Quantization and Motion Law for Ginzburg–Landau Vortices},
  author={Didier Smets and Fabrice B{\'e}thuel and Giandomenico Orlandi},
  journal={Archive for Rational Mechanics and Analysis},
  year={2007},
  volume={183},
  pages={315-370}
}
We study the vortex trajectories for the two-dimensional complex parabolic Ginzburg–Landau equation without a well-preparedness assumption. We prove that the trajectory set is rectifiable, and satisfies a weak motion law. In the case of degree  ±  1 vortices, the motion law is satisfied in the classical sense. Moreover, dissipation occurs only at a finite number of times. Away from these times, possible collisions and splittings of vortices are constrained by algebraic equations involving their… 
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25 Citations
Highly Influential Citations
3
Background Citations
8
Methods Citations
4

25 Citations

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We present in parallel an abstract method of Γ-convergence of gradient flows, designed to pass to the limit in PDEs which are steepest-descent for functionals which have an asymptotic Γ-limit energy;…
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