Decay of solutions of a limiting form of Ginzburg-Landau systems involving curl

In this note, we study a semilinear system involving the operator curl in an exterior domain in R3, which is the limiting form of the Ginzburg-Landau model for superconductors in three dimensions for a large value of the Ginzburg-Landau parameter. We prove that this problem has a smooth solution, and it decays exponentially at infinity.