New developments on the Ginzburg-Landau model
This expository paper offers a survey of the most important results obtained in the last years in the study of the Ginzburg-Landau equation and gives answers to some open problems raised by \textit{F. Bethuel}, the author and \textit{F. Hélein} in their monograph ``Ginzburg-Landau vortices'' (1994; Zbl 0802.35142). It is emphasized the importance of notions of ``renormalized energy'' and ``canonical harmonic map'' in the study of the asymptotic behavior of minimizers of the Ginzburg-Landau functional. It is also pointed out that the number of vortices heavily depends on the topological Brouwer degree of the initial Dirichlet boundary data. The paper is excellently written and it is a wonderful invitation for the reader to the study of Ginzburg-Landau equations.
scientific article; zbMATH DE number 828283