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arXiv · 1704.02764

A branched transport limit of the Ginzburg-Landau functional

Sergio Conti·Michael Goldman·Felix Otto·Sylvia Serfaty
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Abstract

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 $\Gamma$-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.

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Sergio Conti, Michael Goldman, Felix Otto, Sylvia Serfaty. 2017-04-10. A branched transport limit of the Ginzburg-Landau functional. https://arxiv.org/abs/1704.02764

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