### Abstract

For any critical point of the complex Ginzburg-Landau functional in dimension 3, we prove that, for large coupling constants, κ = 1/ε; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log r/ε, then the ball of half-radius contains no vortex (the modulus of the solution is larger than 1/2). We then show how this property can be applied to describe limiting vortices as ε → 0.

Original language | English (US) |
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Pages (from-to) | 206-228 |

Number of pages | 23 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 54 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2001 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A quantization property for static Ginzburg-Landau vortices.** / Lin, Fang-Hua; Rivière, Tristan.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 54, no. 2, pp. 206-228. https://doi.org/10.1002/1097-0312(200102)54:2<206::AID-CPA3>3.0.CO;2-W

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TY - JOUR

T1 - A quantization property for static Ginzburg-Landau vortices

AU - Lin, Fang-Hua

AU - Rivière, Tristan

PY - 2001/2

Y1 - 2001/2

N2 - For any critical point of the complex Ginzburg-Landau functional in dimension 3, we prove that, for large coupling constants, κ = 1/ε; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log r/ε, then the ball of half-radius contains no vortex (the modulus of the solution is larger than 1/2). We then show how this property can be applied to describe limiting vortices as ε → 0.

AB - For any critical point of the complex Ginzburg-Landau functional in dimension 3, we prove that, for large coupling constants, κ = 1/ε; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log r/ε, then the ball of half-radius contains no vortex (the modulus of the solution is larger than 1/2). We then show how this property can be applied to describe limiting vortices as ε → 0.

UR - http://www.scopus.com/inward/record.url?scp=18044401803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18044401803&partnerID=8YFLogxK

U2 - 10.1002/1097-0312(200102)54:2<206::AID-CPA3>3.0.CO;2-W

DO - 10.1002/1097-0312(200102)54:2<206::AID-CPA3>3.0.CO;2-W

M3 - Article

VL - 54

SP - 206

EP - 228

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 2

ER -