Existence, regularity, and asymptotic behavior of the solutions to the Ginzburg-Landau equations on ℝ³

This paper studies the solutions of the Ginzburg-Landau equations on ℝ³ in the presence of an arbitrarily distributed external magnetic field. The existence and regularity of the solutions at the lowest energy level are established. The solutions found are in the Coulomb gauge. If the external field is sufficiently regular, the solutions are shown to have nice asymptotic decay properties at infinity.