3D vortex approximation construction and $\varepsilon$-level estimates for the Ginzburg-Landau functional

Carlos Román (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Mathematisches Institut

We provide a quantitative three-dimensional vortex approximation construction for the Ginzburg-Landau functional. This construction gives an approximation of vortex lines coupled to a lower bound for the energy, optimal to leading order, analogous to the 2D ones, and valid for the first time at the $\varepsilon$-level. These tools allow for a new approach to analyze the behavior of global minimizers for the Ginzburg-Landau functional below and near the first critical field in 3D, followed in two forthcoming papers. In addition, they allow to obtain an $\varepsilon$-quantitative product estimate for the study of Ginzburg-Landau dynamics.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Carlos Román. 3D vortex approximation construction and $\varepsilon$-level estimates for the Ginzburg-Landau functional. 2018. ⟨hal-01675771⟩