### Abstract

We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" H_{c2}. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to H_{c2}.

Original language | English (US) |
---|---|

Pages (from-to) | 939-956 |

Number of pages | 18 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 34 |

Issue number | 4 |

DOIs | |

State | Published - 2003 |

### Fingerprint

### Keywords

- Asymptotic analysis
- Phase transitions
- Second critical field
- Superconductivity

### ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*34*(4), 939-956. https://doi.org/10.1137/S0036141002406084

**The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model.** / Sandier, Etienne; Serfaty, Sylvia.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 34, no. 4, pp. 939-956. https://doi.org/10.1137/S0036141002406084

}

TY - JOUR

T1 - The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model

AU - Sandier, Etienne

AU - Serfaty, Sylvia

PY - 2003

Y1 - 2003

N2 - We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" Hc2. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to Hc2.

AB - We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" Hc2. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to Hc2.

KW - Asymptotic analysis

KW - Phase transitions

KW - Second critical field

KW - Superconductivity

UR - http://www.scopus.com/inward/record.url?scp=0038043590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038043590&partnerID=8YFLogxK

U2 - 10.1137/S0036141002406084

DO - 10.1137/S0036141002406084

M3 - Article

AN - SCOPUS:0038043590

VL - 34

SP - 939

EP - 956

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 4

ER -