Une estimée-produit pour Ginzburg-Landau, et application au flot-gradient

Translated title of the contribution: A product estimate for Ginzburg-Landau and application to the gradient-flow

Etienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg-Landau in dimension 2, with and without magnetic field.

Original languageFrench
Pages (from-to)997-1002
Number of pages6
JournalComptes Rendus Mathematique
Volume336
Issue number12
DOIs
StatePublished - Jun 15 2003

Fingerprint

Gradient Flow
Ginzburg-Landau
Limiting
Energy
Estimate
Heat Flow
Vorticity
Vortex
Corollary
Magnetic Field
Converge

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Une estimée-produit pour Ginzburg-Landau, et application au flot-gradient. / Sandier, Etienne; Serfaty, Sylvia.

In: Comptes Rendus Mathematique, Vol. 336, No. 12, 15.06.2003, p. 997-1002.

Research output: Contribution to journalArticle

Sandier, Etienne ; Serfaty, Sylvia. / Une estimée-produit pour Ginzburg-Landau, et application au flot-gradient. In: Comptes Rendus Mathematique. 2003 ; Vol. 336, No. 12. pp. 997-1002.
@article{5886db5b9b9842d3ac3d47fec7ddb553,
title = "Une estim{\'e}e-produit pour Ginzburg-Landau, et application au flot-gradient",
abstract = "We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg-Landau in dimension 2, with and without magnetic field.",
author = "Etienne Sandier and Sylvia Serfaty",
year = "2003",
month = "6",
day = "15",
doi = "10.1016/S1631-073X(03)00224-3",
language = "French",
volume = "336",
pages = "997--1002",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier Masson",
number = "12",

}

TY - JOUR

T1 - Une estimée-produit pour Ginzburg-Landau, et application au flot-gradient

AU - Sandier, Etienne

AU - Serfaty, Sylvia

PY - 2003/6/15

Y1 - 2003/6/15

N2 - We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg-Landau in dimension 2, with and without magnetic field.

AB - We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg-Landau in dimension 2, with and without magnetic field.

UR - http://www.scopus.com/inward/record.url?scp=0042205130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042205130&partnerID=8YFLogxK

U2 - 10.1016/S1631-073X(03)00224-3

DO - 10.1016/S1631-073X(03)00224-3

M3 - Article

AN - SCOPUS:0042205130

VL - 336

SP - 997

EP - 1002

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 12

ER -