Global solutions of the evolutionary Faddeev model with small initial data

Abstract

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space ℝ1+n to the unit sphere $$ \mathbb{S} $$ 2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.