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arXiv · 1611.02732

Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents

Yaniv Almog·Leonid Berlyand·Dmitry Golovaty·Itai Shafrir
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Abstract

In this work we consider a reduced Ginzburg-Landau model in which the magnetic field is neglected and the magnitude of the current density is significantly stronger than that considered in a recent work by the same authors. We prove the existence of a solution which can be obtained by solving a non-convex minimization problem away from the boundary of the domain. Near the boundary, we show that this solution is essentially one-dimensional. We also establish some linear stability results for a simplified, one-dimensional version of the original problem.

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Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir. 2016-11-08. Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents. https://arxiv.org/abs/1611.02732

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