On a system of multi-component Ginzburg-Landau vortices

TL;DR

This paper investigates the asymptotic behavior of multi-component Ginzburg-Landau equations as a parameter approaches zero, showing convergence of minimizers to solutions of generalized harmonic map equations.

Contribution

It establishes the local convergence of minimizers of multi-component Ginzburg-Landau equations to generalized harmonic maps as the parameter tends to zero.

Findings

Minimizers converge locally in $C^k$-norms

Limit solutions satisfy generalized harmonic map equations

Provides rigorous asymptotic analysis for multi-component systems

Abstract

We study the asymptotic behavior of solutions for $n$-component Ginzburg-Landau equations as $\ve \to 0$. We prove that the minimizers converges locally in any $C^k$-norm to a solution of a system of generalized harmonic map equations.