Geodesic
Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation
Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 177-217.

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We study vortices for solutions of the perturbed Ginzburg-Landau equations Δu+ε21​u(1−∣u∣2)=fε​ where fε​ is estimated in L2. We prove upper bounds for the Ginzburg–Landau energy in terms of ∥fε​∥L2​, and obtain lower bounds for ∥fε​∥L2​ in term of the vortices when these form “unbalanced clusters” where ∑i​di2​=(∑i​di​)2.
DOI : 10.4171/jems/77
Classification : 35-XX, 00-XX
Keywords: Ginzburg-Landau equation, Ginzburg-Landau vortices, vortex dynamics, vortex collisions 
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     author = {Sylvia Serfaty},
     title = {Vortex collisions and energy-dissipation rates in the {Ginzburg{\textendash}Landau} heat flow. {Part} {I:} {Study} of the perturbed {Ginzburg{\textendash}Landau} equation},
     journal = {Journal of the European Mathematical Society},
     pages = {177--217},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2007},
     doi = {10.4171/jems/77},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/77/}
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Sylvia Serfaty. Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation. Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 177-217. doi : 10.4171/jems/77. http://geodesic.mathdoc.fr/articles/10.4171/jems/77/

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