Global solutions to vortex density equations arising from sup-conductivity

Nader Masmoudi; Ping Zhang

doi:10.1016/j.anihpc.2004.07.002

Global solutions to vortex density equations arising from sup-conductivity

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	441-458
Number of pages	18
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	22
Issue number	4
DOIs	https://doi.org/10.1016/j.anihpc.2004.07.002
State	Published - 2005

Keywords

Hydrodynamics
Renormalized solutions
Superconductivity
Vortex density
Young measure

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

Access to Document

10.1016/j.anihpc.2004.07.002

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",

note = "Funding Information: Nader Masmoudi is partially supported by an NSF Grant and by an Alfred P. Sloan Fellowship. Ping Zhang is supported by NSF of China under Grant 10131050 and 10276036, the innovation grants from Chinese Academy of Sciences. The authors would like to thank Professors Fanghua Lin and Qiang Du for some discussions about the mathematical models.",

year = "2005",

doi = "10.1016/j.anihpc.2004.07.002",

language = "English (US)",

volume = "22",

pages = "441--458",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

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

N1 - Funding Information: Nader Masmoudi is partially supported by an NSF Grant and by an Alfred P. Sloan Fellowship. Ping Zhang is supported by NSF of China under Grant 10131050 and 10276036, the innovation grants from Chinese Academy of Sciences. The authors would like to thank Professors Fanghua Lin and Qiang Du for some discussions about the mathematical models.

PY - 2005

Y1 - 2005

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

AN - SCOPUS:18844433317

SN - 0294-1449

VL - 22

SP - 441

EP - 458

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 4

ER -

Global solutions to vortex density equations arising from sup-conductivity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this