Global solutions to vortex density equations arising from sup-conductivity

Nader Masmoudi, Ping Zhang

Research output: Contribution to journalArticle

Abstract

In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of W1,p and Cα solutions to a modified model, which is derived from the physically sign-changing vortices case.

Original languageEnglish (US)
Pages (from-to)441-458
Number of pages18
JournalAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume22
Issue number4
DOIs
StatePublished - Jul 2005

Fingerprint

Renormalized Solutions
Global Solution
Conductivity
Vortex
Vortex flow
Superconductivity
Global Existence
Existence and Uniqueness
Model
Family
Necessity

Keywords

  • Hydrodynamics
  • Renormalized solutions
  • Superconductivity
  • Vortex density
  • Young measure

ASJC Scopus subject areas

  • Analysis

Cite this

@article{9d5189df53dd4d2d8f6f5044466d6417,
title = "Global solutions to vortex density equations arising from sup-conductivity",
abstract = "In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of W1,p and Cα solutions to a modified model, which is derived from the physically sign-changing vortices case.",
keywords = "Hydrodynamics, Renormalized solutions, Superconductivity, Vortex density, Young measure",
author = "Nader Masmoudi and Ping Zhang",
year = "2005",
month = "7",
doi = "10.1016/j.anihpc.2004.07.002",
language = "English (US)",
volume = "22",
pages = "441--458",
journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",
issn = "0294-1449",
publisher = "Elsevier Masson SAS",
number = "4",

}

TY - JOUR

T1 - Global solutions to vortex density equations arising from sup-conductivity

AU - Masmoudi, Nader

AU - Zhang, Ping

PY - 2005/7

Y1 - 2005/7

N2 - In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of W1,p and Cα solutions to a modified model, which is derived from the physically sign-changing vortices case.

AB - In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of W1,p and Cα solutions to a modified model, which is derived from the physically sign-changing vortices case.

KW - Hydrodynamics

KW - Renormalized solutions

KW - Superconductivity

KW - Vortex density

KW - Young measure

UR - http://www.scopus.com/inward/record.url?scp=18844433317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18844433317&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2004.07.002

DO - 10.1016/j.anihpc.2004.07.002

M3 - Article

VL - 22

SP - 441

EP - 458

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 4

ER -