On compound vortices in a two-component Ginzburg-Landau functional Stanley AlamaLia BronsardPetru Mironescu 35J5035J5735Q56Partial Differential EquationsCalculus of VariationsBifurcations We study the structure of vortex solutions in a Ginzburg-Landau system for two complex-valued order parameters. We consider the Dirichlet problem in the disk in $mathbb{R}^2$ with symmetric, degree-one boundary condition, as well as the associated degree-one entire solutions in all of $mathbb{R}^2$. Each problem has degree-one equivariant solutions with radially symmetric profile vanishing at the origin, of the same form as the unique (complex scalar) Ginzburg-Landau minimizer. We find that there is a range of parameters for which these equivariant solutions are the unique locally energy-minimizing solutions for the coupled system. Surprisingly, there is also a parameter regime in which the equivariant solutions are unstable, and minimizers must vanish separately in each component of the order parameter. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4737 10.1512/iumj.2012.61.4737 en Indiana Univ. Math. J. 61 (2012) 1861 - 1909 state-of-the-art mathematics http://iumj.org/access/