TY - JOUR

T1 - Large vorticity stable solutions to the ginzburg-Landau equations

AU - Contreras, Andres

AU - Serfaty, Sylvia

PY - 2012

Y1 - 2012

N2 - We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter ε, inverse of the Ginzburg-Landau parameter Κ, tends to 0. We treat the case of N as large as | log ε|, and a wide range of intensities of the external magnetic field. The vortices of our solutions arrange themselves with uniform density over a subregion of the domain bounded by a "free boundary" determined via an obstacle problem, and asymptotically tend to minimize the "Coulombian renormalized energy" W introduced in [14]. The method, inspired by [22], consists in minimizing the energy over a suitable subset of the functional space, and in showing that the minimum is achieved in the interior of the subset. It also relies heavily on refined asymptotic estimates for the Ginzburg-Landau energy obtained in [14].

AB - We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter ε, inverse of the Ginzburg-Landau parameter Κ, tends to 0. We treat the case of N as large as | log ε|, and a wide range of intensities of the external magnetic field. The vortices of our solutions arrange themselves with uniform density over a subregion of the domain bounded by a "free boundary" determined via an obstacle problem, and asymptotically tend to minimize the "Coulombian renormalized energy" W introduced in [14]. The method, inspired by [22], consists in minimizing the energy over a suitable subset of the functional space, and in showing that the minimum is achieved in the interior of the subset. It also relies heavily on refined asymptotic estimates for the Ginzburg-Landau energy obtained in [14].

UR - http://www.scopus.com/inward/record.url?scp=84887830081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887830081&partnerID=8YFLogxK

U2 - 10.1512/iumj.2012.61.4818

DO - 10.1512/iumj.2012.61.4818

M3 - Article

AN - SCOPUS:84887830081

SN - 0022-2518

VL - 61

SP - 1737

EP - 1763

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 5

ER -