Global Solutions of Evolutionary Faddeev Model With Small Initial Data

Abstract

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space ${\mathbb{R}}^{1+n}$ 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.

Cited by in corpus (1)

• On a non-linear sigma model of knotted relaxed states far from thermodynamic equilibrium in plasma physics and beyond