A branched transport limit of the Ginzburg-Landau functional

Sergio Conti (1) , Michael Goldman (2) , Felix Otto (3) , Sylvia Serfaty (2, 4)

1 Instutute for Applied Mathematics [Bonn]
2 LJLL - Laboratoire Jacques-Louis Lions
3 MPI-MiS - Max-Planck-Institut für Mathematik in den Naturwissenschaften
4 CIMS - Courant Institute of Mathematical Sciences [New York]

We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via Γ-convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.

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

Sergio Conti, Michael Goldman, Felix Otto, Sylvia Serfaty. A branched transport limit of the Ginzburg-Landau functional. Journal de l'École polytechnique — Mathématiques, 2018. ⟨hal-01503958v2⟩