Large-Data Global Well-Posedness for the (1 + 2)-Dimensional Equivariant Faddeev Model

Abstract

The Faddeev model is a classical field theory that models heavy elementary particles by knotted topological solitons. It is a generalization of the well-known classical nonlinear sigma model of Gell-Mann and Levy, and is also related closely to the celebrated Skyrme model. The global well-posedness of the quasilinear PDE arising from this model has been studied intensely in recent years, both in three and two spatial dimensions. In this paper we introduce a proof of large-data global well-posedness of the two-dimensional Faddeev model under the equivariant hypothesis.