Vortices in the Magnetic Ginzburg-Landau Model

• Main Authors: Sandier, Etienne (Author), Serfaty, Sylvia (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2007.
• Series: Progress in Nonlinear Differential Equations and Their Applications ; 70
• Subjects: Mathematics.; Functions of complex variables.; Partial differential equations.; Physics.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.; Functions of a Complex Variable.

With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in superconductivity, superfluidity, and Bose--Einstein condensation. This book presents the mathematics of su...

Table of Contents:

• Physical Presentation of the Model—Critical Fields
• First Properties of Solutions to the Ginzburg-Landau Equations
• The Vortex-Balls Construction
• Coupling the Ball Construction to the Pohozaev Identity and Applications
• Jacobian Estimate
• The Obstacle Problem
• Higher Values of the Applied Field
• The Intermediate Regime
• The Case of a Bounded Number of Vortices
• Branches of Solutions
• Back to Global Minimization
• Asymptotics for Solutions
• A Guide to the Literature
• Open Problems.