Global nonlinear stability of one kind of large solutions to evolutionary Faddeev model

Abstract

It is well known that there is few results about the global classical solutions to quasilinear wave equations with large data. The famous evolutionary Faddeev model corresponding to maps from the Minkowski space $$\mathbb {R}^{1+n}$$ to the unit sphere $$\mathbb {S}^2$$ is satisfying one kind of quasilinear wave equations. In this paper, we show the global nonlinear stability of one kind of nontrivial and large classical solutions.