Vortex dynamics of the anisotropic Ginzburg-Landau equation

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Ginzburg-Landau equation in a smooth bounded domain Ω ⊂ R2, that is, and conclude that each vortex bj(t) (j = 1,2, …, N) satisfies where We prove that all the vortices are pinned together to the critical points of a(x). Furthermore, we prove that these critical points can not be the maximum points.