Asymptotic behaviour of global vortex rings

In this paper, we are concerned with nonlinear desingularization of steady vortex rings in R3 with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti-Rabinowitz condition. Some qualitative and asymptotic properties are also established.