%0 Journal Article
%T Energy and Vorticity of the Ginzburg-Landau Model with Variable Magnetic Field
%A Kamel Attar
%J Mathematics
%D 2014
%I arXiv
%X We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming that the strength of the applied magnetic field varies between two characteristic scales, and the Ginzburg-Landau parameter tends to $+\infty$, we determine an accurate asymptotic formula for the minimizing energy and show that the energy minimizers have vortices. The new aspect in the presence of a variable magnetic field is that the density of vortices in the sample is not uniform.
%U http://arxiv.org/abs/1411.5479v1