Stability in 2D ginzburg-landau passes to the limit

Sylvia Serfaty

doi:10.1512/iumj.2005.54.2497

Stability in 2D ginzburg-landau passes to the limit

Sylvia Serfaty

Mathematics

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

Abstract

We prove that if we consider a family of stable solutions to the Ginzburg-Landau equation, then their vortices converge to a stable critical point of the "renormalized energy." Moreover, in the case of instability, the number of "directions of descent" is bounded below by the number of directions of descent for the renormalized energy. A consequence is a result of nonexistence of stable nonconstant solutions to Ginzburg-Landau with homogeneous Neumann boundary condition.

Original language	English (US)
Pages (from-to)	199-222
Number of pages	24
Journal	Indiana University Mathematics Journal
Volume	54
Issue number	1
DOIs	https://doi.org/10.1512/iumj.2005.54.2497
State	Published - 2005

Keywords

Asymptotics
Ginzburg-Landau
Stability
Vortices

ASJC Scopus subject areas

General Mathematics

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10.1512/iumj.2005.54.2497

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AB - We prove that if we consider a family of stable solutions to the Ginzburg-Landau equation, then their vortices converge to a stable critical point of the "renormalized energy." Moreover, in the case of instability, the number of "directions of descent" is bounded below by the number of directions of descent for the renormalized energy. A consequence is a result of nonexistence of stable nonconstant solutions to Ginzburg-Landau with homogeneous Neumann boundary condition.

KW - Asymptotics

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KW - Stability

KW - Vortices

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Stability in 2D ginzburg-landau passes to the limit

Abstract

Keywords

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