On the dynamics of Ginzburg-Landau vortices in inhomogeneous superconductors (Q1852687)

The paper deals with the study of the dynamical behaviour for the Ginzburg-Landau system. The main novelty of this paper is the presence of a non-constant potential \(a(x)\). Combining several classical methods arising in the Ginzburg-Landau theory of superconductors, the authors prove that in the anisotropic case considered in the paper, the vortices are attracted to the minimum points of the potential \(a(x)\). The proofs rely on variational methods combined with standard elliptic estimates.