We study vortices for solutions of the perturbed Ginzburg-Landau equations where is estimated in . We prove upper bounds for the Ginzburg–Landau energy in terms of , and obtain lower bounds for in term of the vortices when these form “unbalanced clusters” where .
These results will serve in Part II of this paper to provide estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat-flow, which allow to study various phenomena occurring in this flow, among which vortex-collisions; allowing in particular to extend the dynamical law of vortices passed collisions.
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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. J. Eur. Math. Soc. 9 (2007), no. 2, pp. 177–217DOI 10.4171/JEMS/77